Ruthie .... I don't know of any way to rejuvenate these... I had to break down and buy a new one recently....I bought one that is usable on both sides this time....so now when I finish using it, I hang it up with the side I was using facing out and then I know to turn it to the other side the next time I go to use it...that way one side isn't taking all the beating.
I had BIG chips coming off my old one so was running into those with the cutter and ruining my blades.... you may find that you go thru blades less often with a new mat too!