You need to recognize the ship when it is operating on it's (flipped) damaged side as well.
So a ship counter with, say a 12 hull damage factor takes 12 hits, gets flipped and can take up to another 12 hits...
In my original design I actually had two scans of each ship (one undamaged and one damaged with the yellow strip at top)...but flipping the card to its damaged side became too cumbersome and unnecessary.