After you capture a field, the only thing that will immediately repair themselves will be the field acks. Any destroyed structure such as the fuel/ammo bunkers or hangers will stay down until fresh supplies are flow in (this cuts down on the down time of the destroyed structure) or letting time fix (think it's 15 minutes for hangers and 45 minutes for ammo/fuel/barracks) the destroyed structures.
This is pretty much covered
here.
Ack-Ack