Refugee From Time

Characters that are tied to a particular period of history and tend to remain tied to it even as the passing of real time would tend to make them die of old age, or the passing of Comic Book Time would tend to shift them to a later period. It is essentially the hardest aversion of the Sliding Time Scale applied to just one character, normally occuring when the time period becomes highly emblematic of the character or is needed to provide a strong point in their characterisation.

This trope is invoked every time you see an adult in their forties, fifties, or sixties complain about the music the kids are listening to these days. The original fans of rock and roll, even assuming they were all fifteen back when rock began, would be in their sixties today and anyone who grew up listening to punk rock in the late 70s would think today's music tame by comparison.

This causes problems of logic for when the Refugee From Time ends up inside a Sliding Time Scale. By all Fridge Logic the person should be older or even dead, they may at one point follow what should be the time and then flip back to pick up some attributes from another time. At some point the character may have started aging naturally before they realised that it wasn't going to hold. For example, Magneto's backstory involves being in the Nazi concentration camp at Auschwitz. Each new iteration shifts his age down, with Applied Phlebotinum providing excuses for him to be magically or scientifically rejuvenated.

Occasionally a significant cultural event will become such an important marker that its appearance in fiction seems to completely detach it from the normal timeline and have it follow around any character it can find. Woodstock would have to have been held within a TARDIS to cover all the fictional characters that have claimed to be there. Wars are another matter. Rather unfortunately the regular appearance of wars give writers the chance to continuously update their veteran characters.

Examples of Refugee From Time include:

Comic Books

Captain America will always be a result of the World War II Super Soldier program. The time he was trapped in the ice in the Atlantic will just become longer.
Nick Fury is likewise always a WWII vet, but he got some Super Soldier Serum-Lite (an annual injection of the Infinity Formula) that keeps him biologically the same age. (Referring to the main Marvel Comics universe.)
The Punisher is always a Vietnam Vet no matter how many years have passed. He has died and come back to life twice (once when he became the Angel-Punisher, and once with the Frankencastle scenario), with both returns de-aging him (the Angels wanting him to suffer more and the process naturally aiding his health respectively). As of 2011 The Punisher's origin has officially been updated to make him a Gulf War vet.
Over in the DC Universe, the Justice Society always fought in WWII (although some of it's more popular members, such as Superman or Wonder Woman, have been retconned out in various ways), so usually there is a plot device to have had them not age in the decades between the end of the war and the beginning of the "modern" age. This sometimes causes problems in regards to their non-super supporting cast, though only Post-Crisis (when they were placed into the same sliding-timeline-only universe as their JLA cohorts). Pre Crisis, the JSA members all aged in real time on Earth-Two (while Earth-One, like the current DCU, has a sliding timescale). Thus, Earth-Two's Batman and Catwoman had a daughter in the late 50s, who grew to adulthood by the 70s stories she debuted in. As the Huntress.
It has become an established part of Scrooge McDuck's past that the character took part in the Klondike and Yukon Gold Rush—currently more than a hundred years ago. Don Rosa fixed this problem, at least in his own comics, by establishing that all his McDuck comics take place during the late 1940's and early 50's. Thus Scrooge could very well have taken part in the gold rushes as a young man. Some other McDuck authors follow this, but others ignore it and set their stories in the present.
Magneto's backstory is so entrenched in Auschwitz by this point that writers struggle with keeping him as a Holocaust survivor and still keeping him and his contemporary Charles Xavier up to date. There have been attempts to retcon this, but they always Snap Back in the end. The solution seems to be giving Xavier and Magneto anti-aging treatments periodically.
The Simpsons Comics: Radioactive Man started out fighting Nazis in the 1940s (as his Golden Age counterpart, "Radio Man"), but by the time he was finally reunited with his long-lost parents in 1996, he was still only about 25 years old rather than the 80-something years he should have been by that point—and, of course, his mother and father would most likely have been centenarians at the youngest, but in 1996 they were still middle-aged. (Justified in the mother's case, as she was turned into a cyborg by the Nazis and is thus presumably semi-immortal.) RM briefly lampshades this: "Gee, I've been in my twenties for a long time. No wonder I never get any birthday presents."

Comic Strips

Dick Tracy, astonishingly, still occasionally makes reference to fighting Nazi spies like Prune Face and the Brow during the second World War.
Inverted in Doonesbury, which does not use a sliding timescale: every character ages in real time, except for Uncle Duke, who has been around 45 years old since the 1970's. None of the other characters seem to have noticed this, and it's never been explained.
Curtis's father still hates all the "rap stuff" the title character likes, despite by current standards he should have grown up on hip hop.
Similarly, Jeremy's parents in Zits are firmly children of the sixties; this gets harder and harder to reconcile as time goes by (his mother would have had to have given birth to him in her mid to late 40s by now). Maybe they're New Age Retro Hippies.

Literature

In Something Fresh, the first Blandings Castle novel, PG Wodehouse stated that Lord Emsworth had been at Eton in the 'Sixties (that is, the Eighteen-Sixties). Assuming he was as young as possible (13) in the very last year of the decade (1869), this would still mean that he would have been 122 years old at the time of the publication of the last book, Sunset at Blandings in 1978.
The secret agent Quiller was mentioned in the first book written in 1965 as a veteran of clandestine service during World War II. In the last book written in 1996 Quiller Balalaika, he's still a secret agent. He's been an active (very active, as he beats up young guys constantly) for over 50 years.

Live-Action TV

One review of Thirtysomething and similar shows that complained that if the characters had actually been hippies in The Sixties they would have been fortysomething by the time the show aired. The "surprisingly young person who allegedly went to Woodstock" seemed to be a trope well into the 90s actually. Note that around the time of the Woodstock festival, being a "hippie" was (paradoxically) starting to become quite fashionable, and many magazines aimed at younger teenagers who were still too young to truly rebel encouraged them to wear the stereotypically hippie clothes. It's quite plausible that many of these kids identified themselves as hippies, even if they did not yet understand exactly what the hippie lifestyle entailed. As for "being at Woodstock," well, anyone can lie.

Music

Kind of related, though song lyrics can't normally be updated: the song "Hotel California" becomes even creepier as the time period implied by "We haven't had that spirit here since 1969" increases. And even more so when you listen to the full lyrics and realize that the eponymous hotel can be taken as an allegorical version of Hell.
Again, 1969: "Summer of '69" by Bryan Adams was written by two people. Jim Vallence wrote a nostalgic piece that was going to be just called "The Best Days Of My Life" until someone looked at a line and said Throw It In. The piece was always going to have that nostalgic tone (with some Getting Crap Past the Radar with the line "me and my baby in a '69") but the audience ages and attitudes would change slowly. Bryan Adams on the other hand, has now started stating that the '69 was always meant to be about the sexual position with it meant to be bleedingly obvious. This feels a bit more like a shoehorn to keep the lyrics relevant and make it a justified Refugee From Time. Although for Adams, who was only 10 years old in 1969, its entirely possible the song means to him precisely what he says it means.

Western Animation

On South Park, a flashback in one episode showed Stan's mother and father as having been to Woodstock in their youths, while other episodes show Stan's uncle Jimbo was a Vietnam War vet. Meanwhile, Stan (and his older sister Shelly) are perpetual children/pre-teens, which makes this problematic as time goes on (or not, given the bizarre nature of their world).
The Simpsons
- You have Grampa Simpson, who will always be a World War II vet.
- And the Vietnam veteran Seymour Skinner.
- Montgomery Burns has Victorian-era memories that would have made him absurdly old when the show began. Which is yet another case of Flanderization on the part of the Trope Namer. In the 1990 episode "Simpson and Delilah", Burns tells Homer that he's 81 years old, which would place his birth date in 1908 at the earliest. He then shows Homer some old photos of him in college, and the 1920s look to the pictures would have been plausible for an 81-year-old man who probably would have graduated from college in 1930 or so. Burns's age was then exaggerated in later seasons, so that by the mid-'90s Burns was telling people that he went to a college reunion in 1939, met his old sweetheart, discovered she had a young adult daughter, took her (the daughter) to see Gone with the Wind and then to a history museum, and then had sex with her inside one of the museum's exhibits and fathered a bastard child (his then-fiftysomething son, Larry). In order for all of that to have been possible (and to avoid being Squick-inducing), Burns would have had to have been born in the 1890s or possibly earlier.
- Waylon Smithers, Burns's manservant, was originally supposed to have been born in 1954, which would make him a year or two older than Homer originally was. However, a much later episode that flashes back to The Seventies shows him as a baby.
- Marge's mother, Jacqueline, once said that she was arrested for indecent exposure in 1923. But going by the original time frame of the series, Jacqueline couldn't have been born any earlier than about 1915—and it's hard to imagine an 8-year-old getting arrested for public indecency, even back in the day.
- Homer's mother protested against biological weapons testing in The Sixties, but—again, going by the series's original continuity—she would have been well into her thirties by that time and probably wouldn't have been trusted by the younger radicals.
- In the recent episode "The Color Yellow", Bart and Lisa discover that their great-great-great-great grandfather was a black slave named Virgil who escaped to Canada in the 1850s. Going by the current time frame that fits (Virgil would most likely have been in his twenties then), but by the series's original continuity Virgil could conceivably have been their great-great-great grandfather—thus making Bart and Lisa one thirty-second black instead of one sixty-fourth!