A/C not working

No leaks, charge is good (44psi when comp is running), no codes showing when scaned. I tried changing out the compressor relay. This is what has me baffeled and thinking it's something in the climate control.

I have been trying to diagnose my a/c system problems for a few days now with no luck. When I start the car in the morning the a/c clutch engages and the system cools fine for 20 minutes or so. When the car warms up however the clutch will disengage, sometimes it will come back, sometimes it wont. It has gradually gotten worse where it stays off longer to now it wont come back at all most times. I don't know if it is a digressive problem or if it is just because it getting warmer now that we are in summer. I have replaced the low side and high side pressure switches. I have also drained the system down and vacuumed the system, no leaks, and recharged. When the clutch is engaged and the compressor is running the truck cools great. The problem seems temperature related. Is there a temperature probe that could be faulty? I know the a/c usually cuts out at wide open throttle so I thought the tps could be bad but this truck has electronic throttle control. I figured if the tps were bad there would be no throttle at all. The car has dual climate control.

Did you fix your ac problem my truck does the same thing.

I switched the relay and the compressor still shuts down when the truck on the road. What should be my next move? Any suggestions will help.

When the truck is idle the compressor is running. When I get the truck on the road, it runs a few minutes and the compressor shuts down not the truck.

I replaced the battery and when I started the truck I noticed a clicking noise, kind of sounds like a blinker. When the clicking noise stopped the air went from the main vents pointed at the driver it went to defrost and will not switch.