Technically shields and ionic should heal up, but its not been coded in - it's just a wish-list type thing listed in the rules at the moment. Might be worth someone suggesting that they actually heal up now.
I'm with Elias on this. Ionic refers to the Ship's electronics, and changing the overall charge of a ship such that the electrons no longer flow properly through the circuits.
I think, come combat, it'd suck considerably if IONIC would have to be repaired in a shipyard/factory instead of regenerating on its own. I think of Ion-shutdowns like tripping the breaker on an electrical circuit, where the ship shuts down the electronic systems to save them from damage due to the overload. The regeneration is explained by a timed process to dissipate the extra 'charge' caused by the additional ions and re-set the 'breakers' so the affected electronics could be turned back on.
No it shouldnt ... every book and game the Ionic Capacity is similar to a EMP blast. If it is knocked down it only temporarily disables a ship or device after a given time Ionic capacity rises on its own and the ship is active again. It wouldnt even make sense as a game feature to only raise if repaired, it would be redundant and unfair as to you can just disable a ship and pick it off without it having a chance to recover. It should be that once you knock it down it becomes nonoperational for a set time and then the IONIC cap comes back to allow the people to fight back or flee