I used to have a chocolate lab that would get dry spots and his fur would fall off in patches. The vet used to give him shots for allergies but it kept happening. One day someone asked me if he might be allergic to his food. I used to buy lamb and rice Eukanuba and switched to a different brand of chicken and rice. Wouldn't you know, all of a sudden he didn't have any more dry patches. I wasted a lot of money on vet bills.
I'm not sure if that's the same situation but it might be worth a try to change his food and see what happens. Good luck!