Dogs get food allergies pretty commonly and from the dogs I've had with them the only good way for them to diagnose it is with allergen removal trials. Science diet makes some good diets for GI problems but with one dog I had we had to go to a specialty duck and rice diet from a small manufacturer. That's been over 20 years ago so I don't remember who made it. They also can have pancreatitis and pancreatic insufficiency similar to what humans can have. Start with a full chemistry panel and CBC including serum amylase levels. Probiotics aren't likely to help. IF he gets better it isn't because of the probiotics. If you're not getting anywhere with it with your current vet, get a different opinion somewhere else.
This time of year I would be worried about pancreatitis.