Going by the other answer that says it can't outrun the sun, so, no more than 24 hours. There's still the question, why didn't they go back and save Sirius from his death. Lets assume that it was possible, why wasn't it done?
The cheap answer is that they didn't have the time turner. It was presumably locked away in Hogwards for safe keepng and not easily gotten to, but lets assume Dumbledore could have gotten hold of it, so hypothetically, Harry has the Time Turner, with Dumbledore's consent. Why not save Sirius?
In the books, Hermione told Harry "Terrible things happen to wizards who mess with time" and Dumbledore told Hermione "you know the rules" - so, there are rules and consequences. That much is clear. I think there was also a "let nobody see you" warning in there as one of the rules.
One problem that immediately stands out is if Sirius isn't part of the rescue party, that is, if they warn him not to go and he doesn't, maybe somebody else dies. Maybe Harry dies. At the very best, there would be one less person for the rescue, with at least a fair chance of somebody else dying.
When warned of his death, Sirius might likely have said "I don't care, Harry is what matters". Warning him might have done little, except perhaps kept his defenses up when Bellatrix was near.
There's also the "let nobody see you" problem. How do they go back in time, tell Sirius not to go and have nobody say to him "Sirius, why aren't you coming? - Harry needs you".
When Sirius and Buckbeak were rescued in the previous book, Buckbeak was changed up but unwatched. Sirius was locked-up in the tower up but unwatched. Rescuing them could be done un-seen. That's more difficult if someone dies in battle with others around.
And there's the moral dilemma. Sirius would not have let his friends go on the rescue without him and if he had, the outcome might have been worse.
In theory, Harry could have gone back to warn himself not to go, but again that breaks the rules. "Terrible things happen to wizards who mess with time"
It seems probable that Harry might ask for the time turner, at least to Hermione if not Dumbledore, because that's who he was, more heart than sense and "save him" would have been the first thing on his mind. Either one of those two would have recognized the situation was one where the time turner would be a terrible idea, as most situations you'd want to reverse would be. Rare situations where the rescuee is alone, and location is known within 24 hours - maybe and even then, using it is risky (and probably illegal).