A friend used potassium permanganate solution to treat tinea on the hands/feet but after some initial success, the tinea seems to be making a comeback. Could the fungus develop resistance to potassium permanganate?
I don't think a fungus would develop resistance to something so quickly.
As Chris suggested in the comments, it could be because "The disinfective effect is based on the production of reactive oxygen species. The problem is that the solutions used for this purposes are not very stable." So, if fresh solution haven't been used, it may be ineffective.
As commented by @inf3rno, fungal infections could be much deeper and hence, "treating" them superficially may not help much.
Fungi cannot develop resistance that quickly. Potassium permanganate is only used to clean wounds. Therefore, the reimmerging of the fungus may be because it wasn't killed in the first place. I suggest antifungal cream should be used generously to kill the roots of the fungus in his hands/feet.