Well, if the fan speeds are all working properly it isn't the FSR. If the compressor isn't engaging, that is why it isn't cooling... the question is why isn't it engaging. It won't engage with no pressure, but going from all to none in 30 minutes would take a very noticeable hole in the system with the pressure hissing out at you, so that isn't likely the case.
You could always take a voltmeter and check for power to the single wire to the compressor when the ac is "turned on". If the 12 volt signal is there and the compressor doesn't engage then you have a bad clutch. If there is no power there, something is stopping the DME from releasing the compressor. (the IHKA makes the request, the DME analyzes the inputs and releases the signal to the compressor) In this case, you could try jumping power to the compressor with a
fused wire to see if it activates and blows as cold as normal. (I say fused wire to prevent melting wires if there is a short)
And I say all this hoping you checked fuses first.
