In my opinion, the air condition shutting off at high speeds, can be because of a blown fuse in your automobile.
The IDL which maintains the cars Revolution Per Minute (RPM), could have got either dirt, dust or oil in the actuator, which could explain why the air condition shuts off at high rpm's.
Since the IAC is directly tied to the engines electrical units, like the air conditioner, it is suggested that the engine caused a plug t
o misfire, causing a break in the current.