I have occasionally had problems with Airport Utility "seeing" the device to be configured. In those cases one of the following will generally fix the problem. In no particular order:
  1. Using a paperclip to force the AE into a factory reset by holding the reset button in until the light flashes rapidly. (The AE has to be plugged in)
  2. Rebooting the computer you are are running Airport Utility on
  3. Use the Mac that is physically closest to the AE for the configuration
  4. Temporarily move the AE into the room where the router is located in order to set it up. Once it is setup you can move in either into the Living room or if there is an intervening room between the router room and living room putting it in the intervening room.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein