Uwe,
I can agree with Ed in that you should check thoroughly for any air leaks, but you description of no air pressure after 20 minutes of idling until you tapped on the governor, and then the air pressure came up, sounds like a bad compressor governor. Because a compressor governor can be problematic to locate when you are one the road, and they are only about $70 or so, I would change it.
I know how problematic it can be locating a governor because last fall, the governor failed on my coach one morning in the middle of Nevada and the closest replacement was a 8 hour round trip in the tow car and over an hour of work in 30 degree weather before I could move the coach to head for warm Arizona.
Gerald