The power to be immortal in that the user does not stay dead. Variation of Immortality.
The user is immortal in the sense that when they do die, they won't stay dead. This can be the result of instant resurrection, being reborn, etc. They can die from any causes, from physical trauma, disease or simple aging, but the user will always come back.
God Tiers (Homestuck). Ability is conditional, and can only truly die a Just or Heroic death.
Humanoid Cylons (Battlestar Galactica) continuously resurrect in new bodies upon their current bodies' deaths.
After being killed by the Daleks and then resurected by Rose Tyler, Captain Jack Harkness (Doctor Who) gained the abillity to come back from death
After becoming a spirit, if Victor's (Hatchet) body is somehow destroyed or "killed", he'll come back because he has to repeat the night he died for eternity until he finds his father.
Mr. Immortal (Marvel Comics) is a Homo Supreme, having evolved beyond death, he will always come back to life no matter how many times he is killed
Nathan Young (Misfits) will always come back to life upon death, no matter how long it takes.
Snow White (Valkyrie Crusade) is an absolute immortal in that while she can die, she NEVER can stay dead, and will always comes back to life, not matter who she dies.
Phantom (Marchen Awakens Romance) cannot stay dead as long as he has the Zombie Tattoo. It’ll take a few years, but Phantom will indeed be eventually resurrected.
After being killed and then reconstructed by the Mysterons, Captain Scarlet (Captain Scarlet and the Mysterons) gained the Mysteron power of "Retrometabolism" which allows him to heal from serious injuries and return from death.