
Years ago (at home) we had a dog with mange, but it was very scabby/flakey skin on his back by his tail. He was given some powdered wash that we bathed with daily and it disappeared (don't remember what it was called) And a few years ago Maddie had a patch on her leg which she bit off her fur, wasn't so much red as just bare skin. Vet did a scrape and treated her for Demodex Mites, hibiscrub (and fuciderm I think?) was the treatment, that cleared up and hasn't returned.
Wonder why your vet hasn't done a skin scrape though? Mind you one of our vets has this passion for anything epidermal (if that's the right term?) and loves getting his microscope out! LOL
Hope you do get it sorted for him this time, poor thing.