Prednisone is not a good thing to be on long term. It undermies the imune system.

Take the dog to a veterinatry dermatologist. They will do skin scrapings for test for a few things. They will try a few different antibiotics and antihistamines. If it is a food related allergy, food trials can determine which food is best for the pet. If it is not a food allergy, there are allergens (I thhnk 41) which they can test for. It will take some time but they can give you answers.

I just went through this with a cat. It took 4 months, and during that time thecat was wearing an e collar because he kept scratching and links until he was bleeding. He is now on a precriptn food -- Royal Canin green peas and venison. Within 3 days I was seeing a BIG improvement. At the end of 2 weeks we took off the e collar. It has now been 2 months. Kitty's skin is clear, coat has grown back in, and everything is fine.

It is time consuming and a bit costly, but well worth it to have a happy, healthy, medication-free pet!