Having had the same problem, I have been reading various articles and found one that really made sense. The rubber backing has an ammonia-like smell which attracts cats to pee there. Their suggestion was to use throw rugs WITHOUT the rubber backing. I tried it and so far it seems to be working.....just a suggestion.
I know when you have cat problems, you're willing to try just about anything...lol.
They are wonderful creatures, but complex and with a mind all their own. :-)