Lots of good info Jaybay!
And as Jaybay has said, If the other dogs in the house hold are not itchy it probably is not the scabies mite which is contagious to all other species, including humans. Demodex mange is relatively easy to diagnose by your veterinarian with some skin scrapings but if complicated with secondary skin infections may have to be diagnosed with a skin biopsy. So of course it is time to take her to the vet. Demodex is usually not itchy unless there is also a secondary staph pyoderma or other skin disease. An accurate diagnosis is required to treat since the treatment, ivermectin can have side effects. Demodex may take a long time to get rid of because treatment is often discontinued before the parasite is completely irradicated. Other possible skin conditions that your dog may have include: Yeast or fungal infections, other ectoparasites, staph pyoderma, or other pyoderma, atopy (allergic skin disease), or food allergy dermatitis. Yes it could be food allergy dermatitis even though you switched back to the prior food. Dogs, if allergic can develop allergies to any component of their foods at any time, although previously not allergic. Depending on where you live environmental allergies can also be implicated. For instance I see lots of dust or dust mite allergies when the heat is turned on in the fall here in the Northeast. Turning on the heat releases an avalance of dust and dust mites from heating ducts. A good veterinarian should be able to sort your dog's problem out. However, there are veterinary dermatologists who can also assist, if needed.
Please let us know how it goes!
Until Dr. Cheng replies, I'll let you know my experience with a chronic mange dog. Travis had mange from the time we found him in the woods at 6 weeks and it 4 years to finally get rid of it. Our vet told us his immune system was so compromised he just couldn't deal with the mange mites. It never got passed on to our other dog.
You need to take your dog to the vet so he can look at a tiny scraping under a microscope to determine 1) if it IS mange and 2) what kind of mite(s) are responsible. If it's sarcoptic mange (scabies) that can get passed on to humans. Just make sure you handle him as little as possible and wash your hands thoroughly afterward.
Mange can be painful, and just generally miserable. Without treatment, the dog develops pain staph infection in the hair follicles as the mites damage them. It is quite a bit easier to treat now than it was 15 years ago. All we had was mitaban dip - really stinky, nasty stuff. Now I understand Ivermectin is the treatment of choice, and is much more effective than the old mitaban. Thankfully, I haven't had a need to find out!
Please take your dog to your vet and obtain a proper diagnosis and treatment. Your dog sounds absolutely miserable, and doesn't have to.