I have installed a a sub-slab radon mitigation system. When I tested if the fan was drawing from below the slab I got a very weak to non-existent pressure; when I immediately opened the door to my basement the draw became very strong. I'm puzzled to why this is.
Radon mitigation is an effort to pull a slight vacuum on an area between your living space and the soils and rock that contain the radon gas. That negative pressure pulls the radon away from your living space. Some fans might lose the negative pressure if they are unable to pull any air from the surrounding soils, it will pull it through the cracks and seams of the basement slab and walls. If your house is sealed up tight enough to notice a difference between having an open door or not, your home may be approaching being too tight. Does the same thing happen when you open an upper level door or window? Does just happen when you open something in the basement?
The literature on radon suggest that you should try to seal any openings in your basement walls and floor to provide that first line of defense between your living space and the soils under your home. If you get that kind of change by opening the door, you probably need to work on those leaks in the walls and floor. There is a lot more information on radon from the rocky mountain states. See http://www.ext.colostate.edu/pubs/consumer/09953.html and our info from Missouri, http://extension.missouri.edu/p/G1968.
That is my best guess on what is going on with your radon system. I really need more information about the design and components of your system to do a good diagnostic job.