Can you use a base's ability twice by returning it to your hand with Mega Mech?
Yes, that would be a valid move as far as I can see (as long as you had another Star Empire card in play to trigger the ability of the Fighter Base).

While there are no rules anywhere that I have found to support or reject this exact scenario, the official Crisis expansion announcement indicates that it is possible:


  Here we see Mega Mech, one of the few cards in the game with the awesome ability to return bases to hand. Sometimes you’ll want to bounce your opponent’s Outpost to let your fleet slam in for big damage, but even cooler is returning one of your own powerful bases to hand so you can play it again!