Ships lose CR after battle. Losing 10%-20% is no big deal, but if it brings you down to 40%-50% range, the ship will perform worse. 20%-40% range is when minor malfunctions happen from time to time, temporarily disabling engines or weapons. 0%-20% range is when major malfunctions happen, more often and potentially disabling weapons for the rest of the battle and damaging the ship itself (which means that low HP ships can potentially die from that). This means that certain ships can handle several deployments in quick succession better than others, typically low-tech ships.
After battles, your ships should be repaired and regain their CR, before they fight again. Repairs can happen simultaneously with regaining CR and are free if that happens. If you are only repairing the ship at maximum CR, you'll still lose supplies as if it was regaining CR, until it becomes fully fixed.
The rate of regaining CR depends on the ship, but as a rule of thumb, smaller ships are fixed faster. It takes just 9 days for a Lasher to go from 0% CR to 70% (standard), but it will take 18 days to fully fix a Falcon. It's nothing if you're travelling in hyperspace, but if you need to fight two fleets in quick succession, you'll have to fight more carefully or deploy fewer ships.
The game tracks the crew, but in campaign map. Insufficient crew complement causes CR to drop and I've noticed that being short single digit crewmen is not bad, but the more you lack, the worse it gets, to the point that it's better to mothball ships if that happens. Getting badly beat up won't affect you immediately in battle, but if you need to fight more than one battle, it's going to hurt.
