Update: We've received word from several readers that the issue seems to be fixed now.
If you're hitting a snag trying to sign into your Microsoft account on Windows Phone 8.1 after a rollback or factory reset, it looks like you're not alone. A number of users have taken to Microsoft's Answers forum reporting issues signing in after either a factory reset or after rolling back from Windows 10 Mobile to Windows Phone 8.1.
It's not clear what's going on here, but it appears to be affecting a pretty large number of people. What makes the issue particularly nasty is that being unable to sign in prevents you from doing simple things like downloading apps from the Windows Store or syncing data from your Microsoft account.
Until whatever is causing the sign-in problems is fixed, it'd be a good idea to avoid factory resetting your Windows Phone 8.1 device or rolling your phone back from Windows 10 Mobile to Windows Phone 8.1. We'll bring you more if Microsoft acknowledges the issue and when there's a fix. In the meantime, let us know if you've encountered the problem for yourself and if you were able to find a way around it.
Thanks to Tanveer H. and JCerna for the tips!