I've been doing a little more thinking about this. So, infinitely producing fighters is probably a bad idea since it would introduce certain balance and economy problems. But as long as you possess a wing of fighters, it would make sense that they could be rebuilt as long as you have supplies and a carrier with enough CR to do so. Really, I think repairing and replacing fighters at the cost of CR and supplies is the way to go. It just makes sense and makes supplies (and supply lines in future builds) more important without making fighters so costly and risky to use.
In the event that a fighter wing is destroyed and you don't have a carrier with enough CR to produce a new wing, I feel that it shouldn't be permanently lost- it would just be grey'd out and undeployable until you can rebuild it.
The way it seems to work now, the fighter wings with more fighters per wing become more desirable because they're more likely to make it back to a carrier and/or survive battles. The optimal way to use fighters seems to be to send them out en masse to minimize the chance that any one wing takes the brunt of the damage. Making repairing and replacing fighters cost carrier CR and allowing carriers to rebuild destroyed fighter wings would encourage using fighters in a less stacked way. They would be more useful in larger engagements without having to devote your fleet composition to using them. Fighter wings with only two fighters per wing wouldn't be more risky to deploy than a wing of Wasps. All in all, it would make fighters more generally useful.
I just feel like it solves several of the issues I have with fighters without introducing any significant ones of its own (although if it does, I'd like to hear them).
EDIT: I feel like I should explain more why being able to replace fighters with CR is a good way of handling this. It throttles how quickly you can replace fighters and fighter wings, it makes sense from a 'realism' perspective, and it isn't prohibitively expensive.
The main costs are the supplies (which admittedly are quite cheap) and the time spent replenishing CR. It doesn't remove the cost of getting fighters (and they could even stand to be more expensive if this change goes through, in credit cost to buy them and possibly supply cost to repair them), but it does remove the credit cost of having to constantly replace lost fighter wings and returning to stations to get some more. More importantly, some fighters are extremely difficult to find, so you run the risk of not being able to replace them at all. For other ships that's fine, but since fighters are so fragile and disposable (and frankly, giving them the survivability stats of a frigate is a bit weird), it makes sense that they should be more easily replaceable.