A unit is disabled for one of its own turns. So...
Ogre shoots and disables a unit.
Other player goes. The unit is disabled.
Ogre goes again - that unit is still disabled.
Other player goes, and the unit recovers.
Yes! What we do is we place a token on the disabled unit when it's flipped to the disabled side. Then the ogre player at the start of every turn removes all the tokens from the board. Then the other player may recover all the disabled units without tokens on them during his turn as usual.
It honestly rarely happens that there's more than a couple at a time on the board but I play with my kids a lot and it saves arguments to have the tokens there!