Fairly common on many vehicles, the plastic actuator gear can 'crack' at the point where it hooks to the blend door shaft. When that happens (*if* that's what happened on yours), the damper actuator gear rotates like it should but the cracked plastic 'opens' up and allows the motor to continue to turn. You hear a 'click' when it skips. Could also be gear teeth stripped too.
That's a problem b/c the computer wants to see the motors stop at the end of the damper actuator stroke (full open and full closed). Since the actuator keeps rotating it never stops ...and the computer doesn't know when the damper has reached full open or closed ...and it gets confused. It probably defaults to a no-cool situation, b/c the computer cant verify the cooling damper door is in the 'cool position'. At least that's a common scenario which often occurs. Many system will stoke dampers full open and full closed upon vehicle shut-off (or periodically) so they are ready to be re-positioned properly the next time ya drive the car. Sometimes you'll hear the dampers and motors moving back/fourth in an effort to find full open and full closed. I have a broken one on one of my Jeeps right now. I've replaced several Jeep actuators, they commonly break (as do the damper doors!!). HVAC systems in modern cars are more sophisticated than many owners realize.
The fix as alrock indicated is to remove the little electric actuator (motor) and carefully inspect it for a crack at the damper mount, or gear teeth, or maybe a faulty motor. Check the damper shaft that it freely swings open and closed and firmly bottoms out at both ends. I would even take a small pliers onto the shaft (use care) ...and make sure at the end travel it is 'firm' and doesn't continue to rotate , like a broken damper might do. Dampers are often made of plastic and can (and DO) sometimes break inside the heater/ac box where the damper door connects to the shaft (which is another story and usually comes with some tears and f bombs!)
Good luck!
