Revival Loophole

Giles: It doesn't matter how long you were gone, Buffy. You were physically dead, thus causing the activation of the next slayer.
Kendra: She died?
Buffy: Just a little.

—Buffy the Vampire Slayer

Something—a piece of Applied Phlebotinum, a prophecy or other mystical event, or possibly just a custom or law -- mandates a death, often the death of the protagonist. Fortunately, whatever it is defines death very specif ically. It means "your heart has stopped beating" or, in some cases, "you can't fog a mirror". If a separate medical intervention ends up succeeding, the original contrivance won't notice or care. Naturally, this plot twist has gotten a lot more common along with such interventions, a case of Technology Marches On making resurrection (once the stuff of miracles) a mere slap on the wrist.

Compare Only Mostly Dead, Flatline Plotline. When this is used to wiggle out of a prophetic death, it's a form of No Man of Woman Born. Tangentially related to Tricked-Out Time, where you rescue someone from the past who was going to die, but in such a way that the timeline is unaltered.

As a Death Trope, Spoilers ahead may be unmarked. Beware.

Examples of Revival Loophole include:

Film

In The Matrix, the Oracle declares that Neo has the potential to be The One, but he's waiting for something. "Perhaps [his] next life." At the end of the movie...
In Final Destination 2, the survivors are told that only "new life" can stop Death coming after them. They take this to mean that they'll be safe if they can stay alive until the pregnant member of the group gives birth to her baby. In fact, it refers to one of the protagonists drowning herself and then being revived.
This is Blackbeard's plan in Pirates of the Caribbean: On Stranger Tides. After hearing a prophecy that says he's going to meet his end at Barbossa's hands, he figures You Can't Fight Fate and rather than trying to avert or avoid the prophecy, he starts searching for the Fountain of Youth so that he can use it to heal himself after it inevitably does happen. It would have worked, had Jack not pulled a Poisoned Chalice Switcheroo.

Literature

In Knight Life by Peter David, a re-awakened King Arthur, now mayor of New York, avoids his prophetic death at the hands of Mordred through some timely emergency medical response after his heart stops.
Peter David seems to like this one. It also happens in The Woad To Wuin, where the main character has to die in order to get the "ring of power" off his privates, so he dies for just a second, and is revived.
This is invoked in The Curse of Chalion by Lois McMaster Bujold. To break the titular curse, someone has to "lay down their life three times". One of the attempts to do this involves repeated drowning; unfortunately, the second time around they can't revive the drowned man, and the end of the book reveals that they were thinking about the curse in the wrong terms anyway.
In Harry Potter and the Deathly Hallows, Harry learns that he accidentally became a Horcrux, which would typically mean that he must die for Voldemort to become mortal. However, certain actions of Voldemort's made it possible for a Killing Curse delivered by Voldemort to destroy the piece of Voldemort's soul without killing Harry.
In The Dresden Files universe, ghosts are created when someone is murdered and their desire for revenge is strong enough. Wizards leave the most powerful ghosts. So, when Harry badly needs support against a killing nightmare in Grave Peril, he lets it strangle him to death, creating a vengeful and very powerful ghost, then Susan resuscitates him with CPR, so both Harry and his ghost can confront and destroy the Nightmare together.
Aslan in The Lion, the Witch and the Wardrobe accepts death in the place of Edmund according to the Deep Magic from the Dawn of Time. But he does it with the knowledge that an innocent who voluntarily dies for a traitor will be revived in accordance with the Deeper Magic from before the Dawn of Time.
Parodied in The Hitchhiker's Guide to the Galaxy, where Hotblack Desiato is "spending a year dead for tax reasons."

Live-Action TV

The season 1 finale of Buffy the Vampire Slayer has Buffy beat a prophesied death this way; the later appearances of slayers Kendra and Faith serve as further confirmation that her "death" really did count as such in a mystical sense.
In the Eureka episode "Try, Try, Again", Fargo finds himself trapped inside a personal shield device that he can't turn off, and that will eventually expand catastrophically. It's powered off his own personal energy, so the only way they can come up with to turn it off in time is to temporarily "kill" Fargo, turn off the shield, and have a set of Magical Defibrillators standing by.
In the Dollhouse episode "The Attic", Echo realizes that the Attic machinery will release her if her heart stops beating.
In the Stargate Atlantis episode "Thirty-Eight Minutes", Sheppard is latched onto by an alien bug that drains his life energy. The only plan he can come up with to save himself is to temporarily stop his heart with a defibrillator, let the bug fall off, and hope that he can be revived after it does.
In Star Trek: The Next Generation episode "Code of Honor", Tasha Yar has to fight to the death with a local. After she wins, the body of the local is beamed to the Enterprise where Dr. Crusher is able to counteract the poison that was used in the fight.
An episode of Da Vincis Inquest has a mob boss serving a sentence of life in prison. After being declared dead for a few minutes during a heart attack, he makes a legal challenge claiming that he's served his sentence and should be released.
There's an episode of Smallville where Tess is being persued by Checkmate, who implanted her with a tracking device powered by her body. Chloe stops her heart with a defibrillator to deactivate the device and (eventually) injects her with something to start it again.
Used in Stargate Universe: The Mole Telford has been brainwashed, and the brainwashing gets broken by him being suffocated to death and brought back to life.
In the Charmed episode "The Power of Two", the Monster of the Week needs to be defeated by a spell that can only be said by someone on the astral plane—meaning that Someone Has to Die in order to say it. Prue uses a potion that stops her heart in order to say the spell and then be revived by CPR.
Xena: Warrior Princess had this happen, as the conclusion of a deathmatch had to be well, death, and Xena didn't want to kill her opponent. She was only dead for a little while.
In Kamen Rider Double, there was a case where Phillip and Ryu need to get a Gaia Memory out of a woman, but they can only get it out if she was dead. So what does Ryu do? Kill her, of course. Then use the Electric setting on his EngineBlade to revive her.
In Tokusou Sentai Dekaranger, we have Tetsu get a mind-controlling alien who can only be removed by death off of Ban by stopping and then restarting his heart with his Lightning Fist.
In the TV special House of Frankenstein 1997, a werewolf is mortally wounded in wolf form, and her boyfriend brings her to the emergency room, where he holds the doctors at gunpoint and lays the unconscious wolf on the operating table. He then makes them wait until the wolf dies and reverts to human form, whereupon he has them revive her. As the wolf aspect of her is now dead, she's cured of lycanthropy when she recovers.
In Fringe in order to stop the destruction of the two universes in the season 4 finale, Walter, knowing Olivia is Bell's power source to destroy the Universes, shoots her in the head, killing her stone dead. After Bell disappears, Walter manages to push the bullet out, allowing the Applied Phlebotinum Cortexiphan to heal the damage done to her and allowing her to come back to life, thus fullfilling September's remark, "In every possible outcome, you have to die"(disputable).
In series 6 of Doctor Who, The Doctor is destined to die at the hands of River Song on a beach in Nevada. His death is a fixed point in time and as such he has to be at the exact location at the exact time his is killed. He escapes death by having a Teselecta, a robot that can take the form of any person, imitate himself whilst taking refuge inside it. He is therefore able to be at the exact spot at the exact time without being killed.

Video Games

in the second BioShock (series) game, Delta will die if Eleanor dies. Lamb smothers her, stopping her heart long enough to cue the death trigger inside Delta even though Eleanor gets better immediately.

Web Comics

In Wapsi Square, while the full details are never given, Monica is able to control the golem girls because her heart stopped when she got hit by a bus. The only existing explanation is given here.
Possibly in Goblins. Dies Horribly is fated to, well, die horribly. So he sacrifices himself to a demon where the contract says his soul will die over and over again, believing this to be his ultimate fate. The demon kills Dies, but due to a Loophole Abuse, the contract is null and void and Dies is brought back. Whether this truly negates his ultimate fate is unknown at this point, but given the nature of this world, even if it does, his chances aren't good.

Real Life

Most countries' legal systems now define "dead" as an irreversible cessation of brain function. One reason this became necessary was that, under older "cessation of heartbeat" definitions, a criminal who'd received a heart transplant could hypothetically have argued that they were legally dead (because their original heart had permanently ceased to beat) and couldn't be prosecuted.