Permethrin is an insecticide that kills on contact. It either works or it doesn't and it is very easy to tell if it's effective by applying a small amount to a group of lice or mites. If they die, it works.
The very few reports I've read on various forum boards of it not working have been from people who do not understand that the chemical only kills live mites and not the eggs the mites lay. The eggs hatch and the bird has mites crawling over them again and the authers of such reports write the chemical doesn't work. The treatment has to be done as a course of applications to ensure that any further mites that hatch from the eggs are killed.