Bathing a dog will do more harm than good unless the baths are given with a medicated shampoo that is designed for whatever the problem is that bothers the dog. Frequent bathing dries out the skin and makes the dog even itchier, so it might be a good idea to try to talk to the dog's owner and dissuade her from the frequent baths. A visit to the vet to at least come up with a possible starting point would also be a good idea. He could have a flea bite allergy, in which case all the bathing in the world is not going to help unless and until the flea situation is taken care of. This involves spraying the house and yard and all the bedding that the dog uses, and then treating the dog itself with a good veterinary flea preparation like Frontline TopSpot or Advantage or something similar. If an animal is sensitive to flea bites, one bite is all it takes to make them miserable, they don't have to be crawling with fleas.
Another area to experiment with is his food. As Margot suggested, try a food that doesn't contain grain and try one that is made from a food that it isn't likely the dog has ever eaten before. Fish and Sweet Potato would be an excellent choice, as would something made from Duck. If a dog has food allergies, they usually respond in a positive way to these two foods. Capsules containing Omega 3 fatty oils also can be a help.
Believe it or not, it is not out of the realm of possibility for a dog to be allergic to meat protein, therefore the fish-based food would be what I would try first. If that's what it is, you should see a difference fairly quickly and can take it from there. Otherwise, the only other recourse would be to go to a veterinary allergist which can run into much, much money. Please let us know how the little dog does.
Ghilly
Poor little dog must be miserable. You don' t give the age or how long this has been going on.
One of the worst case scenarios would be dermatomyositis. Here is one link with some info
http://www.gopetsamerica.com/dog-health/dermatomyositis.aspx
A vet would have to be consulted and treatment begun.
Skin problems are some of the worst things to try and diagnose. Food is usually the fist suspect but it could be caused my contact with something, inhaling something, etc.
I would cut down on the bathing for sure. She might try bathing in an oatmeal shampoo and using a diluted vinegar rinse (if there are open sores, don't use the rinse).
Food - She should try getting a food that is grain free and might try a fish based food like Pro Plan Salmon for sensitive stomachs. Natural Balance Fish and Sweet Potato, etc.
She would start switching foods over a 4-5 day period (mixing half the regular food with half the new food) *Nothing* else should be fed (no other food, table scraps, treats, etc. When dealing with food allergies, you have to follow this regime religiously and it will take some time to see a difference. Is the dog around or laying on grass often? Is the dog sleeping on synthetic materials? Try using only cotton bedding.
I'd tell her to try the food change and see if she notices any improvement. She can also try giving a small amount of Omega 3 or Flax Seed oil daily (small dog, small amount)
Poor little thing must be miserable.