The Clutch may be slipping but this is a variable displacement compressor, the clutch should be on all the time (when the AC button is pressed).

Could be bad HVAC panel sending out signal later than should be.
Perhaps you can remove the HVAC and give it a good clean with compressed air.

__________________
1998 E39 528i 5sp MT
2006 E53 X5 3.0 6sp MT