Your monobelt tensioner is either out of adjustment or done...quite common on M119 motors it would seem. And when the belt's slipping, it'll shut down the A/C every time. Start there and hopefully you'll need go no further. I consider the tensioner a maintenance item and plan to replace it every 50-75k mi. Mine died at 43k mi. on my 500E, and that's essentially the same motor.
All the best, Michael