Food allergy dermatitis can occur to any food substance in the diet, not just protein. A low protein diet is contraindicated. Your dog, if food allergic, may need a diet with a novel protein source (something your dog has never been exposed to before). A grain-free diet is also important. Since grains are high on the allergenic scale.
So I would either get a prescription diet from your vet such as fish and potato, which is a novel protein source (unless you have been feeding fish as a snack), and also grain-free, or you must find an equivalent limited ingredient novel protein diet at a good pet store. Your dog must be fed this exclusive diet with no cheating for at least 8 weeks. If his skin clears up you know that he was allergic to one or more of the ingredients in his previous diet, and you would either leave him on this diet permanently or begin to slowly add individual ingredients to see if he reacts, to determine what he is allergic to. This is a slow process but, the only definitive way to diagnose what he is allergic to, since there is no accurate blood, or skin test for food allergies. Many dogs with food allergies also have environmental allergies, and in this case although your dog's skin will improve on the hypoallergenic diet his skin may worsen slightly during certain seasons, from pollen, for example.
Enviromental allergies can also occur year round if your dog is allergic to something found in the house, such as dust mites or house molds. An air purifier would help for these. Bathing your dog frequently (once per week) would also help since enviromental allergies can penetrate the skin, and if removed mechanically by bathing will not do as much damage.
Lastly, has your vet performed skin scrapings for scabies or demodex mites? Have you tried using the flea and heart worm product: Revolution? Revolution also kills Scabies mites. Good Luck!
My 3 year old chocolate lab had the same problem when she was a puppy, but she had on her chin and top of her head, took her to the vet, he did a skin scrapping and she had mild case of mange, and the vet said we were lucky to catch it when we did, it would of spread to different area, she was on medication for horse, for about 1 month and it never came back, but we did have to spay her because if she had a litter, 1 puppy out of a litter would have mange.