The Captivate should not be showing up like that when you close the application.
Can you reboot your machine, Launch Captivate and close and observe at each step that is it when it appears in Task Manager?
Additionally, try observing if it occuring with any other software too?
I'm still scratching my head on this one. I'm not too technical, and it is not a deal breaker (though it would be nice to have memory freed up.) I consistently go to Task Manager and 'End Process.' If I reboot without ending these processed, Windows XP barks at me and throws a message if I reboot. I'll do some further troubleshooting if time allows.