How can I PERMANENTLY eliminate cat urine odors from carpets?

I inherited my parent's house. My mom had up to 11 cats at one time. While most used litter boxes (and the two that are still there are fairly clean cats), there were a few that would go anywhere BUT the litter boxes. Now, no matter how much I shampoo the carpets, sprinkle with Carpet Fresh and spray with Febreeze, the cat odors return with what seems a vengeance in a day or two. This is killing my estate tag sales and probably also would when I go to sell the house. Short of re-carpeting which I don't want to do at this point since I may be selling it soon, what else can I do to eliminate the eye-watering odors?