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!!