Hi! I have an 03 S Type and the air conditioning blows hard but only stays cold for about 30-45 minutes. The compressor cuts off and won't turn back on until the car is restarted (most of the time). My mechanic is stumped and states it is not the air compressor, the switch or freon. But something is causing the compressor to turn off. Today I turned the air off, then the car, restarted and I saw smoke come from the passenger side of the hood and smoke came through the vents. I also smell a bbq grill (burning) smell sometimes. Right before the air goes warm the air smells stale. Any possible ideas? I have had two garages tell me I have an a/c compressor leak with a 1500 plus expense. My mechanic warns of a rip off.

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This is not a an easy DIY investigation, I'd take it to an a/c specialist - they can evacuate the gas and test the system can hold a vacuum, if it holds the vacuum a simple refill should be enough. This is a £50 operation in the UK.
If it doesn't hold the vacuum, you know there is a leak, they'll refill including a dye, run it for a while then the dye will reveal where the leak is - you can take it from there.
Running low on refrigerant will certainly cause the compressor to stop.