I can imagine the air is being redirected say from the front vents to the floor/defrost vents and that could be a vacuum leak problem (not enough vacuum to properly operate climate control). And the fan, which is electrically controlled would continue to run at the same speed.

But if the fan is in fact stopping...

First I would look at the factory wiring diagrams and see if there is any "energy saving" feature for your specific model which would do this intentionally. On many cars, WOT [Wide Open Throttle] will shut down the AC compressor to give the engine more power. I've not seen one which also turns off the inside fan?

But that can be tracked down with a voltmeter and factory wiring diagrams. Learning how it is supposed to work and then determining if this is a feature or a malfunction.