08 Trailblazer Intermittent AC problems

My Ac comes on normally and will work for about 30 mins, then it just shuts off and blows warm air. If I shut the motor off and restart it, it will work again. I heard it could be the Clutch coil when it get hot will shut off. I have changed a relay also.

have fixed a few dozen Trailblazers and Envoys that have your exact issue- Usually on vehicles with 175,000 miles or more, the a/c compressor clutch air gap wears too wide, it can pull in when cool, but takes more magnetic pull when the system warms up- so it can't. The test is to slam the hood, or to bump front of compressor (I know, it is real tight down there) - when it is supposed to be on but isn't. If it pulls in, then the gap is too wide and a shim behind the clutch driver needs to be removed. On your vehicle, I pull the clutch fan and radiator shroud out to access, then I remove the 10mm bolt and gently pull off the clutch driver, and throw the thickest shim away and re-install everything and it fixes it for another 175,000 miles.

The Stealership will "fix" it for you by installing a new compressor- if you have an extra $800 laying around.