Airport Extreme "works" but shows that it's disconnected from my network in Airport Utility

I did have to change the "Configure IPv6" option to "Link-local only" for both the Bed AirPort Extreme and the Downstairs AirPort Extreme

Now, both of those devices are set up correctly and you should not have the type of problem that you had before. Or, at least you have minimized the chances of the same type of problem occurring again.

I did run the test-ipv6 site and have posted the result below (9/10). Would this be the result of the DNS Server settings as you mentioned above?

The check indicates that your ISP is not yet fully set up for IPv6 with their servers.

Try using the Google DNS servers to see if that will help.

The settings on the Main AirPort Extreme will look like this when you click on the Internet tab:

I have blacked out some of the IPv4 and IPv6 WAN Addresses for security reasons. You do not need to enter anything in the Domain Name box. That will usually populate based on the other settings.

Note that the IPv6 DNS Servers settings have dual colons in some places. Example....2001:4860:4860::8888 The two IPv6 DNS Server numbers are the same.

No changes are needed on the other two AirPorts since they will pick up the correct settings from the Main AirPort Extreme and pass them along to devices on the network.

Symptoms like this are usually the result of incorrect iPv6 settings on one or more of the AirPorts on the network.

So let's first make sure that the Main AirPort Extreme is configured correctly for IPv6. Here I am assuming that your "modem" is just that......a simple modem with only one Ethernet port.....and it is not a modem/router or gateway that would have multiple Ethernet ports. Is that correct?

For now, please power off the Bed AirPort Extreme and Downstairs AirPort Extreme and check the iPv6 settings for the Main AirPort Extreme. The correct setup should look something like this when you select the Internet tab and then select the Internet Options button. Your screen will display different numbers of course.

Note that I have blacked out some if the WAN IPv6 address for security purposes.

If you need to make any changes, go ahead and apply them and then let the Main AirPort Extreme restart.

At this point, you can power up the Bed AirPort Extreme, select the Internet tab and then select the Internet Options button. The correct setup will look like this:

If you need to make any changes, go ahead and apply them and let the Bed AirPort Extreme restart again.

The Internet tab and Internet Options settings for the Downstairs AirPort Extreme will look exactly the same as the Bed AirPort Extreme.

Make any changes and apply them and let the Downstairs AirPort Extreme restart.

At this point, you would want to check to make sure that the network can deliver IPv6 addresses correctly to other clients on the network.

Enter https://test-ipv6.com/ in the address bar of your browser and take a look at the results. Ideally, you would want to see 10 out of 10. Here is what my AirPort Extreme looks like on the same test:

Note that I have blocked out some of the IPv4 and IPv6 Internet address for security reasons.

If you can't get 10 out of 10 when you run the test, it is possible that you might have to change the DNS Server settings on the Main AirPort Extreme to see if that will help out.

Post back if you need more help with this.