Our F4 Boy was quite sick for some time this winter.
He had either gotten into something he should not have had while we were away (we had a cat sitter, but he is a thief), or developed an allergy to his food. We are not sure which. At any rate, we removed the dry food, and the wet food our boys ate, and replaced it with cooked chicken, cooked rice, and cooked turkey, and gradually, over the course of about 8 weeks, he stopped vomiting and having diarrhea (keep in mind, he was going to the vet for hydration under the skin and an anti nausea medicine about 1x every weak, so diet alone was not a silver bullet). We changed his food, and we have been OK for about 2 months now.
Do I know what the problem was, exactly? Nope. What I do know is that he is doing better now, and that is enough to make me, and our vet, happy. I emailed with our breeder, and she was concerned, but again, we have no conclusion. I am sorry to say this, but you may have to be satisfied with a healthy kitty, and not an answer.