I've noticed that many of my new (3.0 or 3.5) players seem overly sensitive to character death. I say overly sensitive since that is part of the game. Heck, Andy Collins said on his website that for his latest campaign he had his players make two characters in case the first one died!
I'm not big on breaking the rules just to try to get someone to play D&D. If I normally fudge die rolls for all players then I would for a new player. I don't, however. I roll my dice where everyone can see them and work hard to make balanced encounters that skilled players can overcome without the need of luck. Bad luck might get them, but I've only seen crits kill two characters unexpectedly in the last three and a half years.
A player that wants to quit due to a character death may also be traumatized by permanent ability drain, level loss, item sundering, and a host of other horrible things that can happen in a game. I don't see how you could fudge things so nothing bad ever happens to a sensitive player. Better to get it over with fast with a quick death, kind of like ripping off a band-aid. That way, they know it is just part of the game and they learn to play better and smarter.