The zvet didn't diagnose mange? Why on antibiotics and Pred? Revolution is a topical treatment, right? A bit surprised he did that with skin irritation but I am not a Vet.
Agree, if it is mange, can be hard to clear up. Did he give you a special shampoo?
What are you feeding? You might want to try a fish based, grain free food. Transition over half old and new food for a few days. If bedding is synthetic material, switch to all cotton or terry cloth. Launder in hot water and do a vinegar rinse.
Mange can be very difficult to eradicate, and in some cases all you can do is keep the dog as comfortable as possible. Know that SARCOPTIC mange can be passed to other dogs AND humans, so find out about this. If your dog has it, then wash your hands after touching the dog. if you have other dogs, there may be a problem. See your vet.