Tangerine Password Query
First, I thought it was some problem with Gnome keyring, so I logged out. Nope. Then I rebooted... nope; Tangerine wanted a password.
So, as lazy as I am, instead of slipping out of bed to restart Tangerine in the desktop PC, I clicked on a desktop icon and fired my preconfigured remote desktop connection and logged into my desktop Windows Vista account. There, upon hovering over Tangerine icon in the system tray I could see the problem: Tangerine reported as being serving two users, which is the maximum number of concurrent users I had set up. So asking for a password is Tangerine's way to say "get lost!".
To solve the problem, but not its cause, I just restarted Tangerine remotely. I couldn't tell which side is to blame for this issue: if the player's DAAP plugins failing to log out from the server, or the server failing to recognize a log out event.
Anyway, now I know the cause and how to solve it from bed, that's enough for me ;-)