Unfortunately, the repair option, which would make sense, does nothing to solve the issue - at least on my end. I did the disconnect from the internet option and it seems to be working fine for the time being. If you don't have easy access to ethernet cables and are on Windows 10 do the following without leaving your seat:
-Find the internet connection icon in your taskbar. If you're wired it looks like a computer monitor with a small cable on the left side of it. If you're wireless it'll be a wireless broadcast signal.
-Right-click and select Open Network & Internet Settings
-You'll see a few images showing your connection status and path of internet, look below all of that and click on "change adapter options"
-Right click on the adapter shown (Ethernet or wireless will be shown) and probably not many other icons, if any (tip: the active one, which you're going for, won't have an "X" over it and if you're wired you'll want to use the ethernet option, wireless connections need right-clicking on the wireless option)
-You should see the very first option on the drop down menu that says "disable" - select this to disable your network adapter and leave the window open so you can come back quickly
-Close out iTunes if it's not already closed
-Re-open iTunes with the network adapter disabled
-Wait a few seconds then return to the network adapter window you were using a moment ago
-Right-click the same adapter and now there should be an option to "enable", click that to re-engage the network adapter and restore internet connection to your computer
iTunes shouldn't prompt you to sign in again. If it does, enter your password. The glitch was the program not accepting your login and constantly flashing the sign in prompt over and over. Hopefully, you will no longer have that issue now and you can browse iTunes without issue.
If you still have the issue, my best advice then is to click "cancel" or the "X" button until the prompt goes away. It resurfaces every 20-30 minutes as best as I can tell if you go that route but the application seems to be fully functional since I'm technically signed in.