strange a/c issue only when hot outside

My 01 Jetta has been giving me grief when the outside temperature is about >95F/35C and the engine is warmed up. Here are the conditions:
-a/c OFF and engine warmed up: radiator fans cycle off and on normally in warm weather
-a/c ON and engine cold and outside temp not too hot (<95F/35C): both radiator fans come on normally and a/c works normally
-a/c ON and hot outside (>95F/35C): a/c comes on normally at start and when engine cold; after engine warms up radiator fans stop and a/c goes off at stop lights and stop/go traffic. Above 20 mph/30kph I can feel compressor kick on and a/c works. At next stop light compressor switches off. All during this time the radiator fans DO NOT run, unless switched on by higher engine temp, at which time a/c again works! I assume this is because the high pressure switch is kicking on and off based on whether there is airflow over the radiator. So my question is why are the radiator fans switching off when the a/c is on AND it is hot outside? All the important a/c components work fine (radiator fans, compressor, pressure switches, engine temp switch for radiator fan) but something is telling the radiator fans to switch off ONLY when the outside temperature is hot and the engine is hot, exactly when you want a/c the most! I've got a hot stretch of days ahead so I'd like to figure this one out - if I wait till September the symptom (95F+) will be gone!
Thanks for any help!
Ken

[guessing] if it's not some temperature sensor reading out of range, must be the fan control module.
We've been discussing failed AC clutches, do the fans turn off when the clutch goes?

There isn't a Temp sensor that turns the AC System off "unless" it would be the ECU reading the CTS, which I doubt.

Stopped at a traffic light on a >95f day will cause pressure to go up in the system to the point that the high pressure switch might be breaking the circuit. Thus, you may have too much refrigerant in the system. R134a Refrigerant is very sensitive to temperature changes. It only takes a few degrees increase in ambient temp to cause the high side pressure to shoot upward fairly quick. I do not recall the pressure required for the high pressure switch to kick-off to break the circuit (pretty high, I thinking). That switch also has a low pressure function too.

Or, your issue could be FCM related (which I doubt)

Or, the left green 30amp fuse might be losing contact due to heat build up while you are sitting at a traffic light. That is a bad design and is carrying a heck of a load on a very small friction fit contact. I replaced that unit a NB about a month ago. The lady said the AC would work for a while and quit then start again... it was that green fuse holder almost burned out.

Thanks much for the replies. The green 30 amp fuse on top of the. battery seems to be the culprit. With the ignition on and a/c button on the fans were not running - it was very hot outside. I removed the fuse and put it back in and the fans went on for a second and then went off. I wiggled the fuse and got it to a place where the fans kept running. So I'm pretty sure the fuse holder is shot. I'll take it apart and confirm, but thanks much!

DO NOT RUN THE AC UNTIL YOU FIX THAT!

The result WILL be coking of the oil in the compressor as the high side will get WAY too hot, which will result in its destruction. It may take a while to be destroyed but it WILL happen if you allow the AC to run when the fans are not working.