I'd think so.
It seems as though the intention of Gentle Repose is to increase the time window for resurrection, in addition to general preservation of corpses. You mentioned this yourself, in the quote
effectively extends the time limit on raising the target from the dead, since days spent under the influence of this spell don't count against the time limit of spells such as raise dead. [PHB 245]
The one caveat I'd impose is the corpse needs to be Gentle Repose'd within the minute in order to still be viable. After that minute elapses (so long as you're using Revivify as your resurrection technique) you're essentially trying to preserve already-spoiled goods.
So, you fought some Vampire Spawn, which have the annoying:
Energy Drain (Su): A creature hit by a vampire spawn's slam (or other natural weapon) gains one negative level. This ability only triggers once per round, regardless of the number of attacks a vampire spawn makes.
Those negative levels provided by the vampire spawn are temporary until after the duration specified and saving throw mechanics. After 24 hours, and after a failed save, they would then become permanent.
Negative levels remain until 24 hours have passed or until they are removed with a spell such as restoration. If a negative level is not removed before 24 hours have passed, the affected creature must attempt a Fortitude save (DC 10 + 1/2 the draining creature’s racial HD + the draining creature’s Cha modifier; the exact DC is given in the creature’s descriptive text). On a success, the negative level goes away with no harm to the creature. On a failure, the negative level becomes permanent. A separate saving throw is required for each negative level.
What does this mean? The character is dead. The temporary negative level remains. The negative level would have to be removed, otherwise he'd just die again.
Raising the character from the dead would have to have a restoration spell handy to remove the temporary negative levels, the same as if it were permanent negative levels.
The temporary negative levels have a 24 hour duration. That duration doesn't wipe itself off the table by character death. If that were the case, then undead with a create spawn ability would never be able to create spawn - as their energy drain attacks would simply go away when the character died.
The only rule supporting spell effects that end upon death, without special text stating otherwise, is a spell effect that require concentration. Obviously, a spell caster can't concentrate when he's dead.
What can you do?
- If the GM considers a dead1 creature, as still a creature, cast Restoration on the dead creature. There's a little bit of precedence to back that up. Raise Dead, for example, says, Target: Dead Creature. Of course, Restoration obviously doesn't have the word dead in front of Target: Creature Touched, but, ask the GM to work with you a little. The worst he can do is say no.
- If you don't have a Restoration spell handy, raise the dead character back to life, and the proceeding round cast Death Ward. That would make the character immune to the negative effects of the negative levels for the duration of the spell. That could afford you more time, especially with multiple castings of Death Ward.
- Raise him from the dead at exactly 24 hours from his death. That would give the party time to rest, have that much more preparation time (i.e. hireling services from a cleric, purchases of scrolls, pray for spells, etc.) and allow the newly raised character, with the negative levels, a quick chance at a fortitude save.
- Wait for the negative levels to expire and become permanent, and proceed to raise and restore as the rules are explicitly clearer on - probably with the assistance of higher level spell caster NPC's in a temple at the next town.
- Make a new character.
1Being dead doesn't say you become an object. It just says you are a dead character. It also doesn't say effects end when you're dead. It does say, if you are raised, you're raised in the same condition as when you died. If you have temporary negative levels when you died, and are then quickly raised, you'd still have the temporary negative levels.
Best Answer
Can you cast Gentle Repose multiple times in order to extend the "revivability" of a body as much as you like?
Let's take a look at the text of the gentle repose spell:
p. 245 PHB
The answer is yes.
As long as you are able to cast the spell again before the duration ends, you are effectively stopping the clock for the 10-day window of the reincarnate spell. Also, take note there is a stipulation in the spell components that the two copper pieces must remain on the corpse's eyes for the duration.
Does this make a character unkillable?
The gentle repose spell does not have an effect on living characters, so this would, in fact, do nothing to make a character "unkillable."
Keep in mind that casting the reincarnate spell on a protected corpse does not guarantee they will return to life:
p. 271 PHB (emphasis mine)
A creature's soul could be prevented from returning to life for a number of reasons in the time between its death and attempted resurrection.