AC clutch stops engaging in hot weather

2000 Jeep Cherokee Classic 4.0L, in Palo Alto, CA.

My air conditioner clutch stops engaging after driving in hot weather.

In hot weather (>80 degrees), when I first turn on the AC it blows nice and cold for up to 30 minutes, after which it gradually gets warmer and then hot air comes out. If I leave the AC on when it is blowing hot air, it will suddenly blow cold again (sometimes it takes a couple minutes for it to work again, sometimes it takes 30minutes). Then the cycle repeats.
The AC seems to be dependent on outside temperature: on very hot days ~95 degrees the AC will only work for ~5 minutes before blowing hot, 80 degree days the AC works longer, limited testing in cooler weather (at night ~60 degrees) AC always blows cold.
When it is blowing hot air, the clutch on the compressor hasn’t engaged.
When the AC is blowing cold, the clutch engages/disengages normally depending on how you set the temperature.
I replaced the low pressure switch, did not change AC function.
I recharged the AC, did not change AC function.
Engine temperature reading always in normal range <210 degrees.
Heater is working normally.

I’m pretty sure the clutch is getting the signals to engage. When the AC is working normally the engine revs slightly higher when AC clutch is engaged.
Likewise, when the AC is blowing hot air and the clutch isn’t engaged the engine revs higher. And if I disconnect either the low or the high pressure switches the engine reduces to normal idling.

My thinking is that in hot weather the compressor is getting to hot and the clutch is seizing?

My advice would be to take the Cherokee in to good independent AC shop and have them check things out. They are the experts.

The idle speed change does suggest that the PCM is actuating the clutch relay. Check the clutch connector for power and ground with a test light to rule out a broken wire.

If there is power the magnetic coil may have an open circuit (when hot) or is too weak.

Take a close look at the clutch, if it looks burned or damaged it may have been slipping. Slipping is usually caused by oil leaking from the compressor shaft. The heat from a slipping clutch will damage the clutch coil making it too weak to pull the clutch plate against the pulley.

If the compressor shaft isn’t leaking you can replace the clutch assembly, if it is leaking buy a compressor with clutch.