How tight is your serpentine belt? If it's loose, and it slips when you start the car, the compressor will shut off. As was the case with my 300E, I didn't know it was slipping because it never squealed, but my tensioner was bad and causing the same problems.
If you have a pulse counter you can also check diagnostic pin 7 on the X-11/2 for fault codes for the AC system.
Also, try and disconnect/reconnect the neg terminal of your battery -- it worked for me.
'01 E430, Sport 72,000 mi
'98 C280, 126,500 mi