Why won't my A/C turn off on my 2006 F-150?

From an electronic point of view, it sounds like a problem within the PCM. There are more electronic modules in cars today than you can shake a stick at. Depending on your year and model, the body control module controls the AC. Since the system sounds like it resets itself when turned off your problem may be there. Unfortunately, checking the PCM usually requires an engine analyzer. And even if you have a PCM sitting around in the garage they usually need to be calibrated. Your problem appears to be straight forward enough. Maybe you can condense your problem to six or sever words and use your browser to check for similar problems. You probably will not get a specific fix, but it will give you an idea where the problem lies.