One way of preventing Dumbledore from using a time-turner is to have the disturbance take place at Azkaban. And after Bellatrix's breakout, it shouldn't be difficult to have him consider another potential Death Eater escape as a matter of absolute emergency requiring his personal intervention.
Of course, Azkaban is the one place Quirrell can't act in directly, so he'd probably want to Imperius an off-duty Auror or something.
In the Azkaban arc, they were able to Time Turn away from Azkaban, do some preparation, then arrive after being informed of the breakout. I don't think this would work to prevent Dumbledore from using a Time Turner to be in two places at once.
New chapter!
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 104.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: