Sounds like a candidate for a troubleshooting segment!TLDR: Problem solved. Acronis True Image Home ver 11 was the cause of the problem.
Turns out the application Acronis True Image Home was interfering with the secondary desktop. I started shutting down apps in alphabetical order hoping to get lucky and it paid off. After I shut off Acronis True Image the password window stopped auto-hiding. It's a very old program. I don't use it regularly and I certainly don't need it running in the background. Problem solved.