I do have one question, the device you are accessing AirPort Utility with, has it been updated to macOS Mojave? Since the update to macOS Mojave 10.14, Apple has removed Back to My Mac. I too have the issue you're mentioning, normally signing back into my Apple ID would resolve the issue, it no longer does. I've found out after toying around with my devices at home that if you sign out of Back to My Mac, the issue goes away. Just simply select your Apple ID, click on the minus ( - ) symbol, and then click Update.
Unfortunately since Back to My Mac has been removed, you will have to utilize other services mentioned in the article I've linked above to perform functions such as remotely using your Mac with Apple Remote Desktop, file sharing with iCloud Drive and sharing your Mac's screen with Screen Sharing. I've never really used the Back to My Mac features often but they have plenty of other solutions natively built-in that it doesn't even really matter it's gone now.
If you have any other questions, let me know! I'll be glad to help as much as I can.
