Food allergies typically manifest as diarrhea, vomiting and sometimes as itching or skin issues. Generally, a cat that has an allergy to a food ingredient will vomit. The vomiting will occur several hours after they have eaten and the vomit will have virtually no whole pieces of food in it, a slurry of partially digested food, stomach acid and other juices.
It is not uncommon for a cat to vomit once in a while, but several times a day is probably a symptom of an allergy. If it is an allergy, the condition will worsen. Within 5 days, your cat will refuse to eat any more of the food. Proteins are the most common allergy causes in pet food. When you choose a new food, choose one with a different protein source from the food that caused your cat's allergic reaction.