From a narrative perspective allowing changes like this is problematic - it would be too easy for the Doctor to fix mistakes and otherwise change the outcome of an adventure he's in the middle of (or just finished). I don't imagine many people would be interested in a show where the main character could easily fix most of his mistakes.
Within the series there is some explanation of why this isn't allowed. First, while some things are mutable and may be safely altered and influenced by a Timelord other things are not safe to interfere with. The 9th Doctor episode Father's Day shows us one potential danger to messing around where you shouldn't be. The very ending of The Fires of Pompeii would suggest there is some wiggle room but it's not something to gamble with. Second, it's extremely dangerous for someone's timelines to cross. Different incarnations of a single Time Lord seem to be an exception to this rule, although even here it's something to be avoided even if it isn't such an immediate threat.
In Adric's case the Doctor has left the ship by the time he dies so he doesn't risk running into himself if he doubles back . . . but I'd guess it's still a bad idea for him to be there when his 5-minutes-previous self is in the vicinity. This risk alone may be sufficient to keep the Doctor away (or to prevent the Time Lords from allowing such things, in Father's Day we're told that the Time Lords can police such things). And if that isn't sufficient we could always say that Adric's fate was sealed, and the Doctor knew he couldn't try and change things without damaging time itself.
While something of a convenient excuse to prevent the narrative issues I mentioned at the beginning at least we have some in-world explanation.
