Sure brings to mind my grandmother's and mother's admonition that pets were animals, and animals needed to stay outdoors. Of course, I don't ascribe to that, and have had to deal with my own pet issues, like many of you.
Cat urine is by far the worst, and you really must catch it early. Even then, if you put your own nose, in the spot, you'll detect traces of the scent, so it's little wonder a cat returns to the same spot. Like others have suggested, I would make sure the cat's health is OK -- some cats develop UTI quite easily from eating the wrong food and not drinking enough water (but you know your cat better than what any of us do, for sure). I also agree with locating a professional as anything you do, will be largely 'diluting' the scent, not necessarily eradicating it.
My elderly dog has gotten so senile, it seems, until half of the time he hardly knows where he is, or what exactly he is doing, and I have one carpet in particular that I have had to clean repeatedly. It is too valuable of a rug to just get rid of. We had the best luck with a dry cleaning method a pro did, and on nice, warm, sunny days, I still carry the carpet outdoors to air-out. For us people, the scent is no longer there, but every dog that comes into the house smells 'something.'
And, my apologies to my mom, bless-her-heart, but I just cannot relegate the dog(s) to the garage or the backyard. These are my babies, you know.