I've had an annoying issue for a while now where Visual Studio won't properly connect to Azure Dev Ops. I had been able to commit my git changes, but I couldn't see the "Related Work Items" in the Changes tab of the Visual Studio Team Explorer.
The symptom was that even though I entered my correct username and password the password prompt would keep appearing. No error message, just was an over friendly dialog that just wouldn't go away.
One reason this may have happened is that my account email address was changed to a different domain.
The solution for me was to follow this post: https://developercommunity.visualstudio.com/content/problem/176730/repeatedly-asking-for-credentials-when-building-pr.html
I deleted all the files under “%LOCALAPPDATA%\.IdentityService”. This cleared all known connections in Visual Studio to any source provider. Afterwards, I was able to correctly login to Azure Dev Ops again. Whew! This is the type of thing that takes time out of our day for no good reason...