Hi. I'm Dr. Gotthelf. I have been a vet for 35 years and I would like to use my experience to help you with your pet's medical problem.
Many cats with chronic diarrhea actually have something called inflammatory bowel disease. This is usually treated with high levels of an anti-inflammatory drug called prednisolone. Some of these younger cats with chronic diarrheas actually have intestinal lymphosarcoma. Has your cat been tested for Feline Leukemia Virus? Sometimes the only way to know the exact cause of the chronic diarrhea (especially if the other cats do not have it) is to do an intestinal biopsy.
OK, good that the cats are tested. Intestinal lymphoma would still be on my list of possibilities. Ask your vet for a course of oral prednisolone to see if it makes any difference. A very digestible home made food may also be beneficial, especially if this is due to a food allergy causing the IBD.
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The prednisolone is making it worse. We now do not know what else to do. She is having about 10 loose bowel movements a day.