For lack of a better explanation, it's a round handheld disk, I got mine at Hancock's, and it's got like a very fine sandpaper type texture. You rub it all over your mat to smooth down any burrs that come from repeated cutting.
Which was another thought about your mat, it isn't worn in the spot you cut in. It doesn't have to be blatantly visible to have developed a groove of sorts.
If all these suggestions don't seem to solve the issue, can you just flip the mat over to use the other side?