Just in time for Christmas, release 7 is now live! It includes background connection functionality, and fixes issues with password authentication.
To enable background connection functionality, open the bottom app bar, and tap “Enable BG connections” in the bottom left hand corner. Then, accept the dialog which asks to allow SSH Terminal Emulator to run in the background. When you connect to a server, it will tell you in the title above the terminal control whether or not it will stay connected in the background.