Hi I work for a vet dermatologist and have some follow up ?s Is there any redness, bumps, itching? I would recommend a full blood work up testing thyroid levels. Could be a number of things but before you jump to thinking allergy you need to rule out other issues. Allergy would manifest itself as a red bumpy bacterial infection (what lay people call a rash) or yeast on the skin. Usually itchy for the dog. If that's not happening then I would think possible thyroid issue which can be tested for in a simple blood test and easily treated with medication. Thyroid usually causes patchy hair loss with no other symptoms. If not that it could be something totally benign like an alopecia x which causes hair loss and pigment change in the skin, it is easily treated with an over the counter melatonin (sleep aid for humans but metabolized differently for dogs and used for skin issues). Mange usually will show other symptoms with hair loss. Demodex would explode with secondary infection, pustules etc. Sarcoptic or scabies is VERY itchy for a dog. Either way get the pup to the vet for evaluation. Mention all these possible things so they thoroughly look at your pup. ACVD (dot) org is a derm website that can locate a specialist in your regional area. It's beneficial to have you vet call for a consult over the phone so they can steer him or her in the right direction. Good Luck!
Sometimes a pet can get red mange, allergies, etc...have you asked a breeder and/or a vet yet? One of mine had mange many years later after he grew up, and vet stated, some dogs are born or carriers and it comes out later...and they got this creme sav, you put on and its better..
I live in TX and we have farm tractor supply house, sometimes you can go into that type of store (you know where they sell shots, meds, for cows and stuff) and find an experienced person, maybe they can show you a better creme..much luck to you and give your pet a hug for me:o)
Let us know how your pet is doing....