Screen Saver oddity

My screen saver is turning on normally, but after a while turns off and the computer goes back to desktop without any input from me. When this happens there is a Norton Internet Security message in the lower right of the screen, but it disappears before I can read it. There is nothing in the Norton history. A look at the performance history graphs shows only one thing unusual; that my idle time is happening almost entirely in small chunks, even when I'm asleep and not at the computer.

 

Anyone have any ideas of what's going on here, if there's anything serious, and how to stop it?