Well I gave up on shaving close a while back. I just use a Remington beard trimmer to shave. Gives a perma 5-o-clock shadow though.

Anywho, if you must have the baby ass face then the beard trimmer will not do. Have you tried shaving after you get out of the shower? This will make your beard a lot softer and your skin more willing to be shaved. Also, it sounds like you might not be cleaning the razor enough. If the razor is all clogged with hair it obviously wont cut. And all of these new 3-4 razor blade things that they are putting out are for the birds. Its just a marketing ploy. People were shaving close with a single switch blades for years. When I have to shave close, I use a Gillette Sensor Excel which is only 2 razors and have never found anything better. Just try softening your beard before you shave and rinse the blade as often as you can in a sink full of water.