Excessive and persistent scratching

Question
We have a Shih Tzu/Poodle mix. He is a 1 1/2 yr old. He is an indoor dog. About 2 months ago he began scratching incessantly to the point of pulling large amounts of hair out.  We took him to our vet who indicated he was allergic to fleas and had some fleas on him. He gave him a shot of cortisone and a prescription of predisone. We had the flea problem in our yard remedied by our pest control company and took care of the few areas that they could be indoors.  Our dog does not have fleas any longer but the scratching has not stopped even with the predisone. He scratches all over his body, not just in one place. Additionally, he licks himself under his front legs and on his chest to the point of turning his white fur apricot colored.  We are at our wits end with his scratching and tufts of fur all over our house. What do you think the problem is and what can we do?  

Answer
I would recommend that you have the dog treated for sarcoptic mange even though the vet cannot diagnose it.  That may be the answer to a nonresponsive dermatitis that won't respond to prednisone. Sometimes a diet change may also help if the dog is food allergic.