Regularly-Scheduled Evil

A killer is on the loose. Sometimes the killer is a person, but more often it's some sort of supernatural monster. Many people... dozens sometimes, and sometimes even hundreds... of people have fallen to this fiend. No one's noticed because the killer only comes out to play every few years, or every few decades, or even every few centuries. Regardless of the time involved, no one has connected this long string of victims.

At least, no one has put two-and-two together until now. Our intrepid hero is the only one clever or lucky enough to connect the dots. Now if he can only convince someone that the same killer who murdered those prostitutes a hundred years ago is the same killer murdering prostitutes today without being accused of being the killer and left unprotected in a jail cell.

A specific type of Vicious Cycle. If the killer is a supernatural being, it is often a case of As Long As There Is Evil.

And this is a Death Trope, so expect UNMARKED SPOILERS!!!

Anime & Manga

 * In the 2003 anime version of Fullmetal Alchemist, Hohenheim and Dante kill people every so often to use as surrogate bodies for their souls. Dante is attempting to start a new and more destructive cycle by.
 * In Higurashi no Naku Koro Ni, the curse of Oyashiro-sama kills 2 people every year. And it's always right around the town's big cotton-drifting festival, and only 1 body is found, and it's always someone related to the dam project.

Film

 * The Creeper in Jeepers Creepers emerges from hibernation every 23 years and feeds for 23 days.
 * The Evil in The Fifth Element is said to return every 5,000 years.

Literature

 * The vampires in Peter Watts's novel Blindsight were like this until humans invented architecture, which killed them off. It Makes Sense in Context.
 * Stephen King's IT does this, with Pennywise only killing every twenty-seven years.
 * In American Gods by Neil Gaiman, Shadow discovers that the disappearance of teenagers over the course of several years in a small town are actually sacrifices to an ancient tribal god that resides in the town. Not even the people in the town know about the dark secret.
 * Appears in a fairly benign fashion in Carpe Jugulum . Every few years the old Count de Magpyr would arise from the grave, probably kidnap some young woman who looked good in a nightdress, then be killed. This went on for long enough and was generally harmless enough that no one really minded.
 * In The Wheel of Time, Ishamael briefly escapes his prison once every thousand years. The first time resulted in the Trolloc Wars, and the second time resulted in the collapse of Artur Hawkwing's empire.

Live Action TV

 * Supernatural has this happen pretty much whenever they investigate a murder, to the point that it's now standard operating procedure for the Winchesters to look for such patterns.
 * Eugene Victor Tooms from X-Files episodes "Squeeze" and "Tooms" comes out of hibernation every twenty years to feed on human livers, a process which has made him functionally immortal.
 * In the Star Trek TOS episode "The Wolf in the Fold", an alien energy being called "Redjac" frames Scotty for murder. Turns out the immortal killer has been going from planet to planet, killing people, for centuries. At one point it was Jack the Ripper.
 * Penn, the serial-killing Puritan vampire sired by Angel, went on murder sprees every ten years or so.
 * Also from Angel, the Mayincatec demon from "The Cautionary Tale of Numero Cinco" returns to eat the heart of heroes every fifty years.
 * Angel himself did this when he was evil. While Angelus cheerfully tortured and killed people all year round, apparently he thought Valentine's Day was special and every February 24th made sure he did something really evil and petty to mark the occasion.
 * The second Kolchak the Night Stalker movie The Night Strangler (1973). Once every 21 years for the last century, an alchemist strangles several women and extracts their spinal fluid to use in an elixir of immortality.
 * The Torchwood episode "Countrycide" has a group of villagers deliberately kidnap the sort of people who would go missing in the countryside every ten years for a harvest.
 * In Buffy the Vampire Slayer, Hansel and Gretel were really a demon that appeared every so often as a pair of murdered children to provoke witch hunts.
 * In the CSI episode "Sweet Jane," a serial-killing dentist (played with chilling effect by the great Ned Beatty) only gets "the urge" every ten years or so. The length of time between murders is one reason it took so long for the police to catch him.
 * In Dexter, Special Agent Lundy becomes convinced that a pattern of murders repeated across the country is one person. The rampage has been going on every few months for over 30 years. The entire fourth season is centered around this mystery.

Tabletop Games

 * In Ravenloft, committing six murders over six days with the fang of the nosferatu grants the wielder Nigh Invulnerability and no aging for thirteen years. The darklord of Zherisia has been using it regularly for over a century as of the adventure Hour of the Knife.

Video Games

 * In Final Fantasy X, the giant monster Sin always returns to wreak destruction on the planet Spira a few years after it's 'destroyed'. But in this case, the people of the world know of it (a giant killer space whale is sorta hard to miss, after all), and its cycle of rebirth is well known. What they don't know, is the very act of 'killing' it is what causes it to be reborn, as whichever Final Aeon is used becomes Sin in its place.
 * Dracula naturally returns every 100 years, As Long As There Is Evil in the hearts of man. This assumes no one tries to resurrect him in an evil ritual, or there isn't a massive surge of evil at the time.
 * The "surge of evil" (the second world war) only summoned Dracula's castle. It took extraordinary effort on the part of Death to actually awaken Dracula.
 * The "hundred year cycle" is broken by the time of Aria of Sorrow, instead replaced with a cycle of solar eclipses.
 * The Reapers from Mass Effect return roughly every 50,000 years or so to wipe out all advanced life in the galaxy before returning to dark space as they have for at least 37 million years. Nobody puts two and two together because they go out of their way to make sure no definitive proof of their existence is left after their centuries-long genocides. Luckily for the galaxy, the last guys to get the treatment left a little something special for the future civilizations...
 * The Reapers are also shown shape the galaxy to fit this method. For instance, they seeded the galaxy with enough technology to accelerate the development of space-faring civilizations, but not enough that the civilizations can begin to develop weapons or defenses that might stand up to a Reaper.
 * Most importantly,
 * In Star Control 3, it is revealed that the Orz are scouts for a being/race from another dimension that comes to devour all sentient life in our galaxy every time it reaches critical mass. Naturally the most intelligent guys from the last cycle left clues (then devolved themselves just below sentience).

Western Animation

 * The same thing we do every night!
 * In Hercules, a group of centaurs would attack a nearby village every sunday. The villagers got used to the raids to the point of treating them as an Unusually Uninteresting Sight. Then the centaurs' leadership was taken over by a warlord who suggested that they break out of the pattern.