She could have a skin problem, especially hypothyroidism. A good blood test for that needs to go to one of the OFA-approved laboratories, listed at www.offa.org. Your veterinarian can draw the blood and send it there. The values that need to be checked are Total T4, Free T4 by equilibrium dialysis, and TSH. Those three values give a good picture of the dog's thyroid function.
If the thyroid is low, supplement is not very expensive, but you do need to repeat blood testing to keep the dosage right. If the thyroid is not low, your veterinarian may refer you to a veterinary dermatology specialist.
A dog's skin has cells like human LUNG cells. The skin of a dog is very sensitive and reactive to a lot of things. Certainly diet could be a problem. I like to feed frozen BilJac, but that is not available everywhere. I supplement that with Pet Tabs, vitamin E, multidophilus plus, sodium ascorbate (which is a TOTALLY buffered form of vitamin C--you do NOT want to give dogs ascorbic acid), and a small amount of extra virgin olive oil daily.
What a dog is allergic to can vary enormously. Allergies tend to develop over time, to something a dog has been eating for awhile.
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Kathy Diamond Davis, author, "Therapy Dogs: Training Your Dog to Reach Others," 2nd edition, and the free Canine Behavior Series articles at http://www.veterinarypartner.com/Content.plx?P=SRC&S=1&SourceID=47
