Air conditioner compressors usually fail due to one of two conditions: time and hours of operation or abuse. The most likely cause of an automotive air conditioner cooling problem is no refrigerant in the system, if the refrigerant leaks past a leaky compressor or O-ring
The compressor can fail in many ways. It can fail to open, fail shorted, experience a bearing failure, or a piston failure. First check the compressor engagement. If the magnetic clutch is not engaging when the A/C is turned on, the problem may be a blown fuse or a wiring problem.
When troubleshooting you should always think, if there is no cooling problem in the cooling system. If there is, you need a set of A/C service gauges.
A short can be there due to bald bearings. The rotor damages insulation and the compressor fail to function.
If the compressor locks up mechanically and fails to run, you will know because it will buzz very loudly for a few seconds and may shudder until the thermal limiter cuts it off. If there is no acid it is best to replacing the compressor and that is a good plan.
Usually when a short occurs, it is not immediately a hard short one. The compressor torque drops sharply every time a short occurs. The compressor will shudder enough to remove the short.
A clogged filter should be taken as positive evidence of some failure in the system other than a compressor failure. Generally, it will be metal fragments out of the compressor that clogs the filter.
Mechanical wear in old systems internally shows that it is “worn in” and needs more torque to start against the system load than can be delivered. The compressor will buzz loudly like a locked bearing for a few seconds then the thermal limiter will kill it.
And this, in a nutshell, is what can happen to an air conditioner compressor and what you can do about it.