I have one of those big 36" x 54" no-name translucent gridded plastic cutting boards that I bought at JoAnn's. It's nice and big. But when I rotary cut on it, my blades get dull ever so fast.
By way of contrast, I have a little 12" square June Tailor cutting board, and I've been cutting little blocks on that for a very long time and my blade is still ok.
So... is it the board that is the problem?