I understand why the 10th Doctor had to wipe Donna's mind; or else she would burn from having a Time Lord consciousness. However, in the 5th season episode "Flesh and Stone" the Doctor suspects that the events of "Stolen Earth" and "Journey's End" never happened because of the cracks in time (Daleks stealing Earth and their plan to use the reality bomb). Therefore there would have been no reason for the Doctor to wipe Donna's mind. So what happened to Donna?
Donna is fine, and her memory is still wiped.
This is because the events of "Journey's End" still technically happened. As we've seen, the cracks work in such a way that even when they erase something from existence, that thing's imprint on causality remains. It doesn't make much sense logically, but that's paradoxes for you.
In the same way that the events of "Journey's End" can still have happened even after the event itself was erased from history, the Byzantium remained crashed even after the Weeping Angels who crashed it were erased, Amy continued to exist even though her parents were erased, and Rory's engagement ring stayed on the TARDIS even though he was erased.
There are a number of other examples, but the point is that the cracks create contradictory paradoxes in that even though things are being removed from time, their effects on the timeline are not. Therefore, Donnna would still have had her memory wiped because the events that caused that to happen, though erased, still had an effect on the timeline.
The only thing that "fell through the cracks" was the explanation of why Amy seems to have missed so many events of Earth history, like having no idea what a Dalek even is.
In the case of Donna Noble, they made it a joke how she was out of town every time there was an invasion of London over the past couple of years. But they set up the question in Amy's first episode, and never really explained it.
We also never found out why there are no ducks in the Duck Pond.
If you want to make a guess, you could suggest that the Crack in Amy's house kept her, and all of Leadworth, in a slightly altered timeline where the larger alien-related events never happened. Since Amy would eventually be the person to enable everything to be fixed, you could argue that the Universe would somehow find a way to keep her safe from undue harm until such events could come to pass. So after Big Bang Two, much of Leadworth's timeline snapped back to "normal" Amy's parents were no longer gone, etc. But the timeline of the rest of the world remained largely unchanged.
Not the truth, only a theory that fits the facts at hand.