Brad,
I rarely 'log out' and often have a web browser open to the website, so it looks like I'm actually on most of the time.
I believe that until you go to a different website, it thinks you're still on. If you go elsewhere, then I believe it thinks you left and won't show your name at the bottom.
I think that logging out clears the cache of your cookie id, and since I use dedicated PCs (just me), I don't worry about logging out.