Ok thank you. If the stool has been loose to the point it is oozing out and going on for this long then we have to get some testing done. The anal glands can cause similar problems, however unless there was infection it should not last this long.
The first thing we would start with in our office is sending a stool sample out to the lab.A basic parasite panel would be ok but considering the length if time I would suggest discussing running a full PCR panel which checks for the most common parasites, protozoa, and bacteria . The following link will explain this type of test in full detail LINK
If the stool tests fine then we would consider things such as a food allergy/sensitivity or IBS. In our office if the stool was normal we would then try a diet designed for food allergies but we have to be sure the stool is clear of parasites, protozoa or bacterial infection first.
I would give your vet a call and ask about having the stool tested. Until you can get this done I would also suggest trying some probiotics daily. The pet store will carry a product called Forti Flora which is a great probiotic for cats.
If the stool tests normal please let me know and I will me more then happy to discuss the next possible steps with you.
Please reply back if you have additional questions and I will be happy to continue. If you have no additional questions please take a few moments to provide a rating. Please know that providing a rating does not close the question and we can continue to chat as long as needed.