The "online" status appears by your username, and you show up in the "who is online" listing, ONLY if you have clicked on a link on this site within the last 20 minutes or so. If you are not actively clicking things on the site, your online status disappears. You don't have to logout for your online status to disappear.
Many people think you are "online" all the time if you stay logged in, or if you have a window open with InGender -- this is NOT true. You are only online when you're clicking. Otherwise, I think the "who is online" list would be a mile long!
Hope that helps,