I had a lot of trouble with the ruller slipping when I first started making quilts. Part of the problem was that I was holding the ruler down too far from the edge. I think I was paranoid about cutting myself. I have learned to move my hand closer to the edge when holding the ruler down and it seems to help. And if you're cutting a longer strip, just walk your fingers up the edge of the ruller and you cut to be sure you have enough pressure.
Another thing that was causing me problems was that I was pushing too hard against the ruler with my rotary cutter because I was worried I would stray away from the ruler and end up with a wonky cut line.
Oh, and I use the Invisigrip as well - haven't had any problems with it slipping. I have some rulers with the little sandpaper dots and that works well too, except that you have to lift your ruler rather than slide it across the fabric because the sandpaper catches.