I have found that using username@servername as the username for connecting will fix the issue when it happens against Azure databases. I’ve had connections that have historically worked without doing this suddenly stop and then this has fixed it for me.
For instance, when using a login of mylogin and connecting to myserver.database.windows.net, if I instead use mylogin@myserver.database.windows.net as the username I won’t get the “Source is unavailable” issue.