That button controls 2 electric motors, 1 controls the height of the lumbar support and the other controls the dept of the frame that makes the lumbar support. The motors seem simple electric motors so they must be very reliable.
If you can't listen to them working, the problem must be just electric connections or a fuse. If you hear them working, the nylon gear that splashalot mentioned is very weak and can break if you push too hard against the seat back.