I am not sure what is the SPECIFIC cause of this or your dog's allergies, there could be many different reasons your dog has these allergy issues. food can be a big part of what causes allergies to get worse.Sometimes the food they changed works for a bit then something is triggered to make it come back, i am not sure why exactly maybe like they get immune to it after a while or it wasn't the right food in the first place and the steroids helped to mask the symptoms. make sure the treats you give him don't have something he is allergic to in them, cus then the whole point of a allergy free diet becomes silly :P
also make sure you haven't used any new products in your house or yard that could make his situation worse by irritating his skin. sometimes we don't realize that the new different product for cleaning (as an example) we used has an effect on the skin since we always use cleaning products on areas of the house.
use a mild soothing shampoo when bathing. oatmeal shampoos are mild and gentle on skin.
did you go to a specialist? a dermatologist? i am not sure if that is what you meant by "other vet". A dermatologist might help you figure out the direct cause of his allergies and help you with a better regimen for it.
also in fall is a big time when allergies show for dogs, after the first frost it might slow a bit, spring is also another heavy allergy season. not sure where you lie if you get frosts tho, or if he has shown heavy symptoms in winter either.
i hope you get some solution to give your pup some relief
i can imagine how frustrating it is for him and you! good luck, let us know how he does!