I built a small carrier to test the fighters. In the first battle they launched normally (but were too slow to effect anything). A few turns later I brought that carrier with me for another battle. This time I couldn't launch. When I attempted to do so, I received a message that the fighters were already launched... which they were not. I've attached a save directly prior to the second battle, process the turn and attack one of the Sulak worlds, though it is possible that exiting and starting again resolves the issue, you could still replicate this if you attack another target a turn or two later.
Ok, we've detected the problem when initializing the fighters for each combat. Its fixed but until the next build becomes available, be sure that the fighters are back to the ship before ending the combat. I send you the save of the next turn after fleeing from the combat (fighters are now in the correct status for future combats). Update: Sorry, the savegame will not work in that version. We'll release a new build soon where this is already solved.