Well, the whole point of prednisone is to stop the itching. If it's not working, it could be because the dosage is too low, or it's something else like mange.
What you're describing sounds like a secondary bacterial infection due to allergies. Blue had it and the antibioitc Simplicef got rid of it. His fur grew back in a few weeks.
Either way, you need to speak with her vet about the prednisone not working. A dog should never itch while on it since the purpose of pred. is to get the allergies under control.