Thanks for the additional information. It is helpful.
Most dogs that are found to be allergic to one thing are often allergic to more than one. Some are allergic to environmental things like dust in the heating system, pollens in the air, molds as well as certain foods. the only way to determine for sure what your dog is allergic to is allergy testing. There are a few types of testing available. One is blood testing and the other is skin sensitivity testing. Once the allergens are identified they can be avoided. If they can not be avoided, desensitization shots can be give. Read more on allergy testing and the shots below.
Desensitization shots can be read about here:
it may even be that the improvement with the food was coincidental and it was actually related to your heating system or another substance or as I mention there is more than one allergen.
Now there is also yeast and staph dermaititis. These skin conditions are generally seen with allergies. Staph usually occurs on the lower regions of your pet and tends to have small pimple type bumps. Shampoo containing Chlorhexiderm and/or Oatmeal can help with this condition. Yeast typically shows as a greasy area that has a sweet musty odor. Sometimes the skin can become inflamed, darker and thickened due to itching. Yeast likes areas such as between toes, armpits and ears. Selsun Blue Shampoo can help with Yeast dermatitis. When shampooing, lather and leave on 15 minutes before rinsing. These shampoos are not meant to be a cure, just a relief until your pet can see a Vet. Benadryl can be given to your dog, the dose is up to 2mg per pound every 8 hours for itching due to allergies.
I wished I could tell you exactly what caused the itch to return but that would just be guessing. I mention the heating system as often we find dust has accumulated in the vents and the heat moves that up into the air.
You can read about allergies here: http://www.vcahospitals.com/main/pet-health-information/article/animal-health/allergy-general-in-dogs/428
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.