Yeah, but the Doctor explicitly says in The End of Time (much as I'd like to write that story out of the canon) that he can die without regenerating. Seems reasonable to me. If you silently walk up behind the Doctor and shoot him in the back of the head, he'd be dead as shit. Makes the drama and tension of the episode thicker if regeneration isn't just a crutch in any fatal situation.
Of course we know that wasn't the Doctor in "Astronaut," but the point is that the perception of the Doctor being dead only works if being fatally shot while regenerating actually would kill the Doctor. If regeneration were a guaranteed ticket out of any and every form of death, then his enemies would never have believed they'd succeeded in killing him. Nagisa, I'm not sure if a bullet to the brain would be a guaranteed kill; we're not talking Sylar here. (Or Claire Bennet, I should say, since Sylar stole that power from her.) Maybe if it were the kind of bullet that tore up the insides of the target with fragmentation and shock waves, that would do it, but if it were a more limited brain injury, it might still allow regeneration. But if he were, say, blown apart in an explosion, or burned up in a fire, or something on a comparable level of bodily dissolution, then yeah, there'd be no coming back from that. (Granted, the Master somehow came back from being vaporized in "Planet of Fire," but I've always taken that to be an aftereffect of the power he stole from the Source of Traken -- which could also explain his ability to survive in gooey snake form in the '96 movie. He wasn't technically in a Gallifreyan body at the time but a Trakenian one, and of course he still had the same face and voice after his, err, recovery, so it doesn't count as a Time Lord regeneration per se.)
It was the Doctor in Let's Kill Hitler, that River/Mels poisoned beyond his Regenerative ability to heal, hence why River had to give up her Regenerations to heal him. So, yea, from this event, every reason to believe the Spectrox Toxin was a concern for Regeneration.
Time Lords can be shot and killed we saw that The Deadly Assassin and another one was knifed in the back, Goth also died of his injuries in that story. Regeneration isn't a cure all and even the Doctor needed a push at times to regenerate.
And, in retconning mode, the fact that he was in a stolen body at the time POSSIBLY explains why the Time Lords can offer him a new regeneration cycle in The Five Doctors, when there's no indication that this can normally be done elsewhere (ie, they can only do it because this body hasn't already regenerated). It clicks in with the theory that regeneration isn't a natural ability, but one that's bestowed on a a newly qualified Time Lord when they graduate - but it can't then be done again.
^^The timelords are quite a greedy bunch when it comes to life extension, they can regenerate 12 times, bypass the 12 limit rule when needed, steal other beings lifes and bodies, and then go and top up on stuff like the elixer of life from the Sisterhood of Karn. lol Greedy buggers. lol
Well, the Master can steal others' bodies, but that doesn't mean all Time Lords can. The Master is an exceptionally evil being, and like the Doctor, he's a renegade who's travelled the universe far more extensively than most Time Lords. As such, he would've sought out techniques and technologies that would increase his power and, if necessary, conquer death. So he could have abilities that other Time Lords don't.
The Master was only able to steal Tremas' body because he still had the residual powers leftover as Keeper of Traken.
See post #62. I've already posited that both his recovery from being vaporized in "Planet of Fire" and his survival after being disintegrated in the movie may have been the result of the same power that he gained from the Source of Traken. I mean, why assume it was a one-time thing instead of a permanent change? After all, this is fantasy, and it's all just handwaves. In a series where Amy Pond can wish people back into existence after they've been erased from time, it's kind of silly to object that any given explanation for the Master's powers is arbitrary or inconsistent. Using the Source to explain all the anomalous things the Master did between "The Keeper of Traken" and the '96 movie is a nice, simple handwave, and Doctor Who is such a fanciful franchise that we don't really need anything more solid or logical than a handwave.