So what occurs when they go back to the destroyed state but no longer qualify to be destroyed?
It already qualified to be destroyed.
We shall see.
It exits the state for being destroyed temporarily but then enters it again but now it does not qualify to be destroyed. Hmmm we shall see how FFG handles that
It does not exit the state of being destroyed at any point. The ship IS destroyed upon receiving damage cards, it is then treated "as if" it were not destroyed, but is still very much destroyed. If you remove damage cards during the Rieekan ability, the ship no longer qualifies to be destroyed, but that doesn't matter because it already was destroyed.
Rieekan's ability triggers specifically on a ship being destroyed, which occurs immediately upon receiving the final damage card, and again there is no condition you can meet which removes the destroyed status. If there were, it would be in the rules reference, and there can't be an "un-destroy" trigger unless FFG adds that in an FAQ.
It doesn't need to re-qualify for being destroyed at any point, since that state never changes once it's applied.
Alternatively, if Rieekan read "The ship IS NOT destroyed until the end of the Status Phase", then sure you could go ahead and repair to your heart's content, but it doesn't say that. (Maybe it will on release, who knows?)