Had one of these fail on my A4 (2006) just before I sold it to buy my A8.
You should find if the pressure sensor has faulted out then they should typically go short to ground as they break up. The plastic body on the back of the sensor goes brittle and breaks up, alloys moisture ingress and they die a slow painful death.
You should see that when it fails the car will default to 'eco' / 'econ' mode to stop the compressor engaging and it won't let you turn eco mode off so have a look in mmi see if it's doing that. If the sensor has gone faulty it'll tell you via a fault code too.
If you do change the sensor make sure you get a good spanner on the pipe before you try to remove the sensor from it. The pipes are aluminium and crazy crazy soft and will twist up so easily you don't want to risk rupturing it. If it does leak it's very illegal and worse still mad carcinogenic heavy gas so get the hell away from it if it goes.
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Current: 2004 D3 4.0 TDI V8 in Crystal Blue.
Factory: finger print, tv, xenons, keyless entry & go, soft close boot, 19s, and probably lots more besides
Done: fixed headlight washer leak, fit Bluetooth in place of factory phone
To do: DAB, DTV, fix soft close boot, get a spare key, investigate NSF bushes,
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