Does Izzy have any tear staining under her eyes?
Do you ever notice her chewing at her feet?Are the patches symmetrical (meaning in the same place on either side of her body)?
Thank you for answering my questions.
Both the tear staining and the chewing at feet are HUGE red flags for a dog who has allergies.
As someone who lives with an allergy dog herself, I can completely understand how frustrating it can be when you're trying to figure out what is causing your dog to be so miserable. I strongly suspect that your little Izzy has had allergies all along, but because she doesn't do a lot of scratching it may have been overlooked as a reason for the hair loss.
With my pup, I had my vet do VARL testing (more info here: http://www.varlallergy.com/ ), which determined exactly what he was allergic to (turns out he's allergic to ragweed and a specific type of pollen), which made it easier to control his contact with the items he's allergic to. As a side note...many, many, many dogs are highly allergic to corn and corn products, so if your dog eats a commercial food with corn in it, that could be contributing to the issue.
We also began using the medication Atopica (more info here: http://www.atopica.com/ ), which helped control his itching and made him a happier guy. Atopica is sort of the 'big gun', and once we got my dog's allergies under control, we were able to switch to Temaril P (http://www.1800petmeds.com/Temaril+P-prod10406.html ) instead (which is less expensive and it only takes 1/4 tablet once a day to keep my dog's allergies in check).
My suggestion is that you call your vet and ask if they think VARL testing and either Temaril P or Atopica is right for your dog.
I hope this helps!!