Symptoms
Air that is not cold, a clutch that cycles rapidly or not at all, a rattle or squeal that appears only with the A/C switched on.
Likely cause
Refrigerant carries the oil that lubricates the compressor, so a slow leak starves it. Running low on refrigerant for a long time is what usually precedes a seizure rather than following it.
How should it be checked?
Check for leaks before recharging. A system that needs refrigerant has a leak by definition — topping it up without finding the leak repeats the failure.
How can you check it yourself?
Run the A/C at full cold with the engine idling and listen at the front of the engine. Then check whether the vents get cold quickly or take a long time.
The question to ask the shop
Has the system ever been opened or recharged, and if so was the receiver/drier replaced at the same time?