If the wood is sound, peel off the carpet (or a patch of carpet), install stainless T-nuts, then glue the carpet back down.
T-nuts - great idea! I think you are talking about the kind that have teeth to bite into the wood to keep from spinning. I will try that if these screws stop holding again. I might also try drilling more holes in the fender to put more screws in. It doesn't seem like there is enough factory drilled holes.