Prednisone is one of those drugs that seem like a miracle at the time, but the longer it is used, the worse the side effects from using it can be. It can cause the adrenal glands to not produce enough cortisol on their own and too much of a build up can cause cushing type symptoms.
So it is something you want to be careful with, even in small doses for prolonged use. I'd probably try what Marianne suggested. Another week on small dose (very small) and then a retest and try to have it off pred completely.

There is also a kind of withdrawal from having higher cortisol that dogs feel, which is like being lethargic, not interested in anything, feeling their aches and pains more. It's usually will pass as natural cortisol levels are maintained, if it is a withdrawal.