I wasn't able to find a canonical answer to this, but I found one that is logical and lines up with the effects of Time-Turners in the books here.
Quoting from that page:
Luckily, time travel in Harry Potter doesn’t exactly work that way.
The time traveler cannot change the past because what is experienced
in the past has already been changed.
So the Ministry would be unable to go back in time and destroy
Voldemort unless they already went back in time and destroyed
Voldemort, thus negating the need to do so.
This lines up perfectly both with the book and movie versions of the events involving the time-turners. Remember in the movie, that Harry, Ron, and Hermione were alerted to the coming of the Ministry officials and Dumbledore when a rock mysteriously flew though the window and hit Harry. Later on, we see Hermione throwing the rock.
The book also falls into this pattern.
Note added for all of those that this doesn't make sense to
In science fiction, there have been several different ideas about what time travel entails. Wikipedia covers them. The time travel described in the Potterverse is described in the first theory listed here. It's not unique to the Potterverse at all.