Whenever I close Banshee by clicking the 'x' in the upper left-hand corner; the player moves to the next track and keeps on playing, just without a GUI. I had this problem in Rhythmbox as well. I'm also having the same problem with Software Center.
It certainly looks like the UI/Window Manager is not always sending the application 'kill' signal to the running process. I'm currently using Gnome 2.x / Ubuntu Classic. I haven't tried this in Unity yet; but I suspect I will have the same problems there as well.
Has anyone else had this problem; and is there a work-around???