Why does a site say I am online and I am not?

Well, what you are seeing is less than frequent updates, IF they even update pages at all after initially loading them. In essence, what you are seeing is a record in a database from when you last were there. The site polls users. It polls every minute, or hour, or day or at whatever interval the site is programmed to do. So, it may update your record when you log in, but not again for a day when it polls to see if you are still there, and THEN updates your status to off line. There is no way of telling how often they poll users to see if they are still online.