Why did my Time Capsule disappear, while continuing to work as wireless router?

My Time Capsule cannot be mounted for backups, and the Time Capsule does not appear at all in AirPort Utility. However I can see and connect to its WiFi just fine. The truly odd thing is that I can connect to it using "Configure other..." in AirPort Utility, and see all of its configuration and backup drive.

Some screenshots follow. First, this is what I see in Airport Utility:

If I hit forget, I get this:

Note that the globe and the nice little green dot and "Internet" is my WiFi connection through the Time Capsule that is not there!

Clicking on "Other Wi-Fi Devices" shows no devices discovered.

If I click on the globe, I see the local IP address for the router, 10.0.1.1:

Now I do "Configure Other..." from the File menu, enter the router address 10.0.1.1, and the Time Capsule password. I get the full configuration of my otherwise invisible Time Capsule!

All of the tabs show the correct configuration. But I still can't connect to the very Time Capsule that I am connected to the internet through!

I have tried power cycling the Time Capsule and computer, and doing a soft and hard reset of the Time Capsule, reloading the configuration from a saved file (using Import and Export Configuration File). I end up right back in the same place.

Does this ring any bells for anyone here?

The same thing happened to me yesterday; I don't know if this will work for you.

What fixed it is as you said go to "Configure Other", then disable Back to my Mac by clicking on the - sign on your email adress. It will reset and then I could see the HDD.

That fixed it for me. Hope it helps!