I used to have similar problems with the razor skipping, stopping etc. because of hair thickness/density and I found the solution is...

...experience. Plain and simple, for those of us with this problem, you have to use a strong yet smooth sideways force to keep the blade moving in combination with a delicately light down force to keep from butchering your face. A technique that only comes with time. (heavier blades help, if you have a chance to get one, I'd recommend it)