I think this one really depends on your quest's design. With that said, in most cases, I think punishing the player for deaths is going the wrong direction. If the player is dying repeatedly, the game is a challenge for them. Making the game harder as a punishment only lower the odds that they'll be able to finish it, creating a rich get richer poor get poorer sort of situation. If anything, I'd argue that a higher death count should result in the game easing up a bit. The goal, generally speaking is for players to see the end of the game.
Now with that said, there are cases where that's not true, where deaths are meant to be a very punishing thing and the emphasis is on avoiding it at all costs. However, that requires a very specific sort of game with a very fine-tuned difficulty, and frankly, that's not typically where ZC quests are at. If you do end up tying something negative to death count, my warning would be to be very, very careful about it and to ensure the entire game is designed around that; it can't just be added as an afterthought.