There's nothing related to clutch cycling in the climate control system that is time based. Generally what happens is that clutch cyling is triggered normally and the compressor triggers the cutout function when it is switched on again. There is more resistance to starting the compressor when the high side pressure is up than when the car has been sitting.

Does the interior fan slow down as the cabin approaches the set temperature, then it cuts out? Or does it cutout while blowing gale force? The former would be expected and point toward the clutch slipping. The latter case is more inidicative of a control problem where the compressor is intentionally turned off due to a fault elsewhere.

In the last year or two I recall a discussion about a very difficult to solve cutout on an older 124. It was similar to your situation in that it was a very consistent time from when the car was started until the a/c shut off. None of the usual suspects were to blame. If memory serves (iffy proposition with me...) it ended up being the evaporator temperature sensor. After a few minute of cooling the sensor went non-linear, causing the CC head unit to think the evaporator was freezing up. The a/c would not come on until the car had sat for a good long time - then it would do the exact same thing.