First, with the engine not running and the AC switched off, measure the gap in the compressor clutch with a feeler gauge. If you see more than about 0.015” gap then the clutch could possibly be worn to the point that it won’t engage when the system calls for it.
The next thing you would try is performed when the engine is warm and you have run the AC to the point it won’t cool. Does the clutch engage when it should? If not, then with the engine running and the AC switched ON, Use a wooden broom stick, or the equivalent, to tap the face of the clutch on the forward half (traveling downward) and see if the clutch will engage and the system produce cold air. If it does engage with the broom tap then we’ll talk about shimming it.