My first basset had some sort of food intolerance, with vomiting and diarrhea. After some experimentation, we found a preparation that she did well on, and we kept her on that preparation for the rest of her life. She lived for another 10+ years. 
From Canine Food Allergies,MYTH: “Soy and corn are common food allergens and it is best to seek pet foods without these ingredients to avoid problems.”
FACT: The most common food allergens for dogs are: beef, dairy, and wheat. These three ingredients account for 68% of canine food allergies.
The digestibility of corn and other foods depends, in large part, on processing. Corn in most commercial dog foods is ground and cooked, increasing its digestibility. Different types of corn products meet different nutritional needs. Some corn products meet carbohydrate needs, some have most of the carbohydrate removed and are a protein source, and some consist largely of fiber.Dogs are not likely to be born with food allergies. More commonly, they develop allergies to food products they have eaten for a long time. The allergy most frequently develops in response to the protein component of the food; for example, beef, pork, chicken, or turkey.