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Is the compressor locked up? What are the pressure readings on the low and high side at idle and at 3K RPM?
First of all little information on how the system works. When the AC comes on either by being in the defroster mode or one turning the air-conditioning system itself on the magnetic clutch relay energizes sending 12 V to the winding of the magnetic clutch. Once the compressor starts to spin there is a rotational sensor built into the air conditioning compressor. That rotational speed sensor has to match the engine RPM if it does not the AC amplifier will shut power off to the magnetic clutch relay. There are only a few things that will cause this the first one is the relay that you said you've already replaced that. I normally tell people to swap it out with the horn relay and see if the problem goes away a lot of aftermarket relays don't work well. The only other option is the compressor itself is starting to lock up or the pressures are too high so that it causes the speed sensor to detect slower rotation of the compressor compared to the engine RPM so the AC amplifier shuts the system off. If there's any belt slippage it will cause the same thing. The magnetic clutch itself is slipping it will cause the same thing. It is one of those three or four areas that have to be checked. It's very rare to see the actual speed sensor itself fail.
Ok see how hard the front of the compressor is to turn with the engine off. Should turn by hand with some resistance.
If his gauges are correct and at idle you have 150 on the high side in 20 on the low side that would indicate that the air-conditioning is under charged. A normal operating system at an average of 80°F ambient temperature will put you at about 220 on the high side and about 32 give or take five on the low side. With the compressor off after about 10 minutes both sides should equalize and be the same if they're not this would indicate an issue with the compressor. He probably didn't wait long enough when he looked at the pressure readings.