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Electrical; check the fuse - footwell #3
Leaks in the lumbar pipes. Its rare for the baladder to leak but the joints in the pipes occasionally fracture allowing air to leak. You can pull back the seat cover with the seat still in the car to access the pipework
I would have to go check, but I don't recall how much sound the pump motor makes. Yes, your pump can be shot. The bladder can be shot too. Not sure about the difficulty factor of accessability. I know for sure there are threads about replacing the bladder with a blood pressure cuff... try a search.
Good luck & let us know how you do!