Airport Utility 5.6.1 (Windows 10) can't find Airport Extreme Base Station

I have model Airport Extreme Base Station (model A1408).

I'm running Apple Airport Utility 5.6.1 on Windows 10.

The Windows 10 firewall is turned off.

All my WiFi devices, including my Windows 10 laptop, all work fine on the wireless network, and the light on the base station is green.

Life seems good... EXCEPT, when I run the Apple Airport Utility (version 5.6.1) it says it is "unable to find any Airport wireless devices". Clicking Rescan doesn't fix it. Power cycling the base station doesn't fix it. It was working before, so it's behavior seems to be somewhat intermittent. Lately, it's not working at all. So, I cannot reconfigure my base station.

Is this a known issue? Is there a known fix?