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Hi I'm Dr. Carole and I'm a small animal veterinarian. I'm sorry to hear about Princess. It sounds like this problem has been going on for quite some time. Cats urinate outside the box for a number of reasons. First of all problems with the urine like a urinary tract infection, bladder or kidney stones or something called Idiopathic cystitis. The last thing is a problem where the bladder becomes irritated and it becomes painful for the cat to urinate. They start to associate the pain with the box so they start to go elsewhere. The infection is treated with antibiotics so if that didn't work then may not be an infection or the wrong antibiotic was given. To diagnose stones you need to do an x-ray. To treat the idiopathic cystitis you give pain medications and I recommend feeding a canned cat food diet, preferably one designed for urine health like Hills C/D. A urine sample would help determine if it is one of these things, not sure what they did at the vet. The urine needs to be taken by a method called cystocentesis where the urine is removed directly from the bladder with a needle and syringe. This ensures it doesn't get contaminated. Bloodwork sometimes get done to rule out metabolic disease like diabetes, thyroid or kidney disease. These conditions cause an increased urine production so the cats need to urinate more often and in larger amounts. Make sure the litter box is getting cleaned twice a day and consider adding a couple more boxes because it could be a behavioral problem. Some cats don't like the litter or the location of the box or the box may be dirty or they just prefer other substrates like clothes. Some of these cats need to be medicated with Prozac to fix the problem. There is also a pheromone spray called Feliway that helps with inappropriate elimination. It can be found on line or pet stores. Works really well.
I also suggest that you look into the website indoorpet.osu.edu. It has great information on how to decrease stress in cats and some think stress causes the idiopathic cystitis and behavior problems with the litter box.
Oh and one more thing this website at Cornell university has great information on cats - vet.cornell.edu