Can a fungus become resistant to a chemical such as 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.