What a shame, poor baby! Seems odd to me. What age was he when you got him?
Are the skin infections on a specific part of the body, and has any hair come off? I guess the vet is working through the big list of causes.. Parasite/flea reaction, auto immune reaction, allergies galore. . Have they tried a simple antihistamine yet? I had a dog with temporary severe skin trouble, when she was ill from something else, and responded to steroids, and a friend whose spaniel reacted to latex dust in balloons.
Vets could recommend an antihistamine which can be bought cheaply at a supermarket, until the cause is found.
What does the ear infection look like? What did they do about it? It's a shame to cut puppy hair short, but it may be the only way to keep the infected areas really clean.