I suppose it is possible for a cat to have a long-term UTI, but I would expect at some point over that excessive length of time for an infection to worsen and have a dramatic negative impact on the cat's health.
It could be behavioral, or it could be a case of .... oh, I can't recall the term, (interstititis? ugh, I know that is wrong!) but it is like bumps or something in the cat's bladder and it makes them behave as if they've got a UTI, but they don't. I also can't recall how vets diagnose that condition.