I have exact same problem. In case this is helpful:
Airport Utility for Windows 5.6.1
Airport Extreme 7.6.4
Issue discovered during scan open of AU
Search response message: RESCAN button, Airport Utility was unable to find any Airport wirelesss devices.
Tried: restarted computer, router, modem. Tried "Configure Other > Choose Base Station: 10.0.1; Password: Public, OK> Scan>Error: "Airport Utility was unable to find your Airport wireless device after restarting"