We are going through something similar with our ~13 year old dog. She developed intermittent diarrhea and vomiting that our attempts to diagnosis were futile. Because of this she also lost a fair bit of weight (5 lbs on a 39 lbs dog). After a few vet visits the vet convinced us to try a special diet which is prescription (and expensive). It is also, like you were told, very strict since as the vet said you don't want to mess up the progress by introducing a variable (treat) and having to start all over again. The dog fortunately loves the new food but I'm sure hates the restrictions. After a bath she usually gets treats and yesterday, no treats, the look she gave us was very much WTF. And so far it has been working but we'll have to wait and see still since it's been less than a week but a good week so far. The vet thinks that something might have changed either in the formulation of the food or in her that doesn't agree with her. She was ok with just chicken, rice and pumpkin but when we started her old kibble to give her a more balanced diet we could only get to about 50% before we would have another incident. This is why the vet thinks it's the food. Also fortunately through out this she has been very good and never had an accident in the house though I was outside at 4am a few nights which was less than ideal for me.
Hope you get to the bottom of it. Our dog also has allergies but they appear to be related to summer in California (she doesn't have problems in the winter or when we go to Washington) so I think it's related to heat or the lack of humidity