Does a fighter or drone ever get replaced when it is lost in battle?
Mid-battle? No. Post-battle, though? Yes; my experience has been that it seems as though carrier fighters are replaced after every engagement, though I've seen others indicate that it takes a turn or two for carrier fighters to be replaced.
Why not allow resupply or ship fabrication to replace lost fighters and drones. After they are destroyed the carrier is basically useless.
If you're suggesting mid-battle fighter replacements, then I'm very much against this. Carriers can already be incredibly strong; improving them by making them spawn replacement fighters mid-battle is completely unnecessary and would require significant changes to the fighter system (not that that'd be a bad thing). If you're suggesting post-battle fighter replacements, this would seem unnecessary to me since in my experience fighters are replaced after every battle anyways, though as I've seen others indicate that it can take a turn or two for fighters to be replaced there may be one or more bugs involved.