I was regressing to childhood and watching old Doctor Who, and I just got to the episode "Earthshock" and the followup in "Time-flight". Tegan basically asks "why don't we go back in time and save Adric?" and the Doctor has a fit.
Normally the show just passes over this sort of thing without comment. Now, I realize that Adric's death is supposed to be really shocking, discombobulating everyone so much that even the Doctor misplaces his theme song! So I guess the writers felt they couldn't just pass without comment in this case, except it's time travel, so there's usually no logic to be found. So the Doctor just emoted his way around it.
Okay, fine, that's the real answer. (EDIT: Yes, also, Adric was a smeghead. Understood, but this isn't Red Dwarf...)
But from what I've seen of this website, you lot are more creative that that :-) So, in-universe, and asking about this specific case, why not?
I get things like: you can't change history, fixpoint cross your own timeline etc etc etc. But why is this such a case? How does the Doctor even know Adric did in fact die? We, the viewers, were shown it, sure. But the Doctor and his surviving companions (Tegan and Nyssa) could not have witnessed that. They only saw the freighter from the outside. They inferred that he died. But how do they actually know he didn't escape at the last minute? And what paradox could result if it was them who popped back in time a bit more to allow him to escape, given that it would not actually change what they had witnessed earlier?
ADDED: about "fixed points in time": the Doctor was not even on board the freighter, in fact, the only witness to Adric's death was Adric. Adric completely failed to affect anything, and his body, and all other evidence that he was there at all, was totally vapourized. Really, this sounds like an example of something that ought not to be a Fixed Point in Time, right?