It's very common for skin conditions to go hand in hand with other problems, such as allergies, endocrine (hormonal) disorders or immune-mediated disorders. If antibacterials did not work then it could be that it's something that is immune-mediated, and these types of conditions are often very difficult to get a handle on. Shih Tzus and Poodles both have a laundry list of genetically passed-on problems, so it's very likely that this is something that your dog has been harboring since birth that has just become apparent. Many genetic problems don't become apparent until the dog's 5th year or later. I would talk to the vet about the possibility of an immune-mediated problem and see what the treatment would be. In many cases it would consist of steroid treatment, but that can be kind of risky because dogs don't tolerate steroids nearly as well as cats do and it often gives rise to other problems involving the liver and other organs, so you have to weigh the pros agains the cons very carefully.
Ghilly