There are many causes of automotive air conditioning problems. This one is interesting because it is obscure, hard to find and in this case, was introduced at the factory from day 1 on this vehicle. Several dealer shops worked on this, in and out of warranty. In the end, each one added some freon and sent the car on its way.
I finally fixed this myself. The root cause turned out to be that the magnetic clutch air-gap was over-shimmed from the factory. See #14 on the exploded parts diagram and the shim discussion.
Here are the clues that lead to this discovery:
The extra shim caused a slightly large airgap. This means that the magnetic force required to engage the clutch is increased from its design goal. At high ambient temperatures, when the engine gets hot, the IR copper losses in the clutch winding increase, thereby reducing the clutch current and the magnetic force. This magnetic force drops low enough to release the clutch even though there is current in the winding. On cooler days, or more airflow (high speed), or before the engine reaches max temperature, there is enough magnetic force to engage the clutch and things work fine.
The key to this was noticing that the clutch would quit spinning while current was still being applied.