Redemption Rejection

When that offer of redemption just isn't good enough. Sure, some people, after a lifetime of committing unspeakable evil, will do whatever it takes to wash away their sins and join the side of good, but not you. No, when Old Lady Redemption offers you that Last Second Chance, you tell her, "Thanks, but no thanks." Then you steal her wallet for good measure.

Tai Lung: All I ever did, I did to make you proud! Tell me how proud you are, Shifu! Tell me! TELL ME!
Shifu: I have always been proud of you. From the first moment, I've been proud of you. And it was my pride that blinded me. I loved you too much to see what you were becoming. What I... was turning you into. I'm... sorry.

Tai Lung: (looks genuinely touched for a moment, then grabs Shifu by the neck and snarls) I don't want your apology! I want my scroll!

—Kung Fu Panda

The reverse of a Heel Face Door Slam. There the bad guy is actively seeking redemption, but is denied it. Here another character or even the universe itself goes out of its way to give someone a chance at mending their ways, only for the offer to be firmly refused. Maybe the bad guy doesn't see themselves as the villain, and so doesn't think redemption is necessary. Maybe they realize their own wickedness, but think redemption is impossible and therefore pointless to pursue. Maybe their motives for doing evil are so powerful they think a guilty conscience is a small price to pay. Or maybe they just have no morals whatsoever and think that Evil Feels Good.

At that point, that's the signal for the heroes to take the gloves off and give the villain what he now most definitely has coming to him.

Essentially a subversion of a Heel Face Turn. Not to be confused with Reformed but Rejected.

Examples:

Anime/Manga

In Soul Eater, Tezca Tlipoca tries to convince former-college-went-rogue Justin Law to come back to DWMA, pointing out that Justin still has chance to redeem himself by providing the info about Kishin's location to DWMA. Tezca also calls him out on living solely by blind faith and cutting himself away from others, and offers to fix that with his friendship. Justin refuses and kills Tezca instead.

Comic Books

The ending of The Killing Joke is along these lines. Batman reaches out to Joker that they've got to stop before one of them kills the other. Joker seems to want to but sadly rebuffs the offer, before telling his famous joke.

Batman: Don't you understand? I don't want to hurt you. I don't want either of us to end up killing the other. But we're both running out of alternatives... and we both know it. Maybe it all hinges on tonight. Maybe this is our last chance to sort this bloody mess out. If you don't take it, then we're both locked onto a suicide course. Both of us. To the death. It doesn't have to end like that. I don't know what it was that bent your life out of shape, but who knows? Maybe I've been there too. Maybe I can help. We could work together. I could rehabilitate you. You needn't be out there on the edge anymore. You needn't be alone. We don't have to kill each other. What do you say?
Joker: No. I'm sorry, but... no. It's too late for that. Far too late. Hahaha. You know, it's funny. This situation. It reminds me of a joke...

Film

In the Godfather movies, Michael is responsible for oh so many murders, earning him quite the guilty conscience. In the third movie a priest tells Michael that he can still make amends for his sins; however, the priest is Genre Savvy enough to realize that Michael won't believe his crimes can be forgiven, and so won't bother changing his ways.
In The Avengers, Thor tells his brother Loki (the villain) that it's not too late to stop his plan after unleashing an army of aliens on New York. For a second it seems like Loki will back down, but then he stabs his brother in the stomach and blows off his offer as 'sentiment'.

Literature

Harold Lauder from The Stand uses this trope when the Boulder Free Zone not only accepts him but begins to regard him as a hero. He realizes full well he has a choice between putting his childish grudges aside forever or holding onto them, even though he knows that they're poison. In the end he decides he's carried his hate for too long to just let it go, and joins up with Flagg.
In The Scarlet Letter, Hester talks Chillingworth into realizing that he has hurt Dimmesdale, but he later ignores that realization.
Lucifer in Paradise Lost - 'he would rather rule in hell than serve in heaven'

Live Action TV

Faith expects this trope to be played out in "Choices," but Willow surprises her.

Faith: Give me the speech again, please. Faith, we're still your friends. We can help you. It's not too late.
Willow: It's way too late. You know, it didn't have to be this way. But you made your choice. I know you had a tough life. I know that some people think you had a lot of bad breaks. Well, boo hoo! Poor you. You know, you had a lot more in your life than some people. I mean, you had friends in your life like Buffy. Now you have no one. You were a Slayer and now you're nothing. You're just a big selfish, worthless waste.

After Angel ruins Jasmine's plan to create world peace at the expense of free will (and eating people), he finds her wandering distraught through LA. She chews him out, asking if her price for ending war, disease and poverty was really too high. He insists that it was, but suggests that she can still try and make the world a better place the old-fashioned way, even if she's lost her powers.

Jasmine: Not all of them. (punches him off a bridge)

Barney from How I Met Your Mother uses this trope quite often. Practically Once a Season there's an episode that focuses on how shallow, selfish, and cruel his life as a Casanova is. By episode's end it looks like he's about to learn an important lesson and be more considerate of women from now on ... and then, without fail, Barney will explain that, no, seducing an endless stream of anonymous bimbos really is all he wants out of life.

Lily: So you made a life changing decision not to change your life at all?
Barney: True story.

Mr. Eko from Lost had a tragic backstory about being kidnapped and made into a child soldier, becoming a criminal, and feeling responsible for causing the death of his brother, Yemi. His main Story Arc on the Island was trying to talk to Yemi's ghost. As it so happens, Yemi was a Catholic priest, so their eventual meeting takes the form of a confession. Eko must be ready to ask for forgiveness, right?

Mr. Eko: I ask for no forgiveness, Father, for I have not sinned. I have only done what I needed to do to survive. A small boy once asked me if I was a bad man. If I could answer him now, I would tell him that, when I was a young boy, I killed a man to save my brother's life. I am not sorry for this. I am proud of this. I did not ask for the life that I was given, but it was given none the less. And with it, I did my best.

- Of course, as it turns out, "Yemi" is actually the Smoke Monster/Man In Black in disguise, and he promptly kills Eko after this. So any future chance of redemption is lost right then and there.
Though the drivers on Canadas Worst Driver and related shows aren't actually villains, there have been two contestants who fit the basic premise of this trope: Colin from Season Two and Scott from Season Six made a big joke of everything and refused to learn. Colin became the first to be expelled from any Driver Rehabilitation Center in the world, while Scott became the first (at least on the Canadian show) to be effectively expelled by his own nominator (who cancelled Scott's insurance, meaning Scott was no longer a valid driver).
Babylon 5 has Londo Mollari, who is told he'll have three opportunities to choose redemption, or suffer the consequences. In a possible subversion, these moments are never directly revealed, and it's arguable whether he's saved his people or condemned them.
Once Upon a Time sees Rumpelstiltskin almost de-powered by Belle's True Love's Kiss... but of course, he has a bit of a freak-out and rejects it. Quite possibly regrets that pretty hard.

Music

In "Reviewing the Situation," from the musical Oliver, Fagin briefly considers the attractions (or lack of same) of a moral and upstanding life, but ends up deciding that a comfortable old age is much more important to him.

Tabletop Games

Lord Soth of Dragonlance could be the poster child of this trope. When the deity Mishakal offered Soth a chance at redemption by stopping the Kingpriest of Istar and preventing the Catacylsm, he initially accepted the request but then put aside his mission to confront his second wife about her infidelity. As a result, he was cursed to become a death knight. While in Ravenloft, Soth was given an opportunity by the Dark Powers to put his evil past behind him; he rejected their offer and was made into the Darklord of Sithicus.

Video Games

In Suikoden IV, there are several moments where Lazlo can offer his former best friend Snowe Vingerhut the chance to join the rebellion. If the player chooses to do so, Snowe angrily rejects it. In their last encounter, this can then be inverted into a Heel Face Door Slam, with Lazlo deciding to execute the now throughly broken-down Snowe.

Western Animation

A truly heartbreaking moment in Kung Fu Panda occurs when Shifu apologizes to Tai Lung for helping to shape him into the monster he's become, saying that his pride blinded him to the fact that his pupil had a few darker tendencies that he should have noticed and possibly fixed. Tai Lung appears genuinely affected for a moment... and then angrily says that he didn't come here for apologies: he only wants the Dragon Scroll. It's at this point when the audience realizes that Tai Lung is truly beyond redemption.
Happens a lot in Gargoyles with Demona, largely because she's the queen of the Ignored Epiphany- she's several times offered a chance to change her ways, but ultimately never repents for more than about a minute. Goliath still seems to wish she'd find redemption, but no longer considers it a realistic possibility.
On the SpongeBob SquarePants episode "F.U.N", SpongeBob tries to make friends with Plankton in the hopes that having a friend will make him stop being evil. Plankton plays along, in the hopes that it will get him to the Krabby Patty secret formula, but he appears to be reformed by The Power of Friendship. Then SpongeBob catches him with a Krabby Patty, and this tearsome confession follows:

Plankton: All right, it's true! I tricked you to get to the Krabby Patty, but then you showed me friendship; and now I realize... that's all I ever really wanted.
SpongeBob: Really?
Plankton: (grabs Krabby Patty) No, not really! Being evil is too much fun!

In the original Ben 10 series, Ben originally offered his enemy Kevin 11 a chance to do good, but the latter refused the offer and attempted to take the Omnitrix. From the on, Kevin was treated as someone who's actions couldn't be redeemable. Still, that didn't stop Ben from making the offer again in the second series. Apparently, after regaining his humanity and getting his head on straight, Kevin became wise enough to accept the offer. It wasn't until recently that it was shown why Ben felt Kevin deserved another chance.
Happens at the end of The Lion King II where Kiara and Zira are both knocked over a ledge during a fight, and are now both dangling over the edge of a waterfall. Zira is gradually slipping off the ledge she is hanging onto, and as a result Kiara tells her to grab onto her paw so she can pull Zira to safety. However, when Zira finally comes up to Kiara she tells her "NEVER!!!" and immediately lets go and falls to her doom in the river below.
Happens near the end of the Transformers Animated episode "Predacons Rising." When Bumblebee discovered that his former friend Wasp has been mutated during a lab experiment while vowing revenge on Bee for (accidentally) imprisoning him for being a spy, Bumblebee feeling guilty about what he did, immediately apologizes to Wasp. Wasp's response? "Wasp... ...forgive... ...Bumblebot... ...BUT WASPINATOR NEVER FORGIVE!!!"
Toy Story: "Where's your kid now, Sheriff?!"

Real Life

The infamous pirate Edward Teach (better known as Blackbeard) was at one point pardoned and had the chance to reform himself. Blackbeard soon returned to piracy and continued to plunder the high seas, and paid for it in what may have been one of the toughest battles the navy ever had to fight against pirates.