Ok, that's a different thing. I suppose you see your user id as logged in but a "Welcome, Guest" at the top. This even happens if you used the logout button. The forum software seems to cache some information to reduce the stress on the underlying database. It synchronizes with the database later, which may look like a logout has no effect. It shouldn't be possible to post a message until you login again though, otherwise this would be a security issue.
If you visit the site after having logged off or with a different browser / a different computer then there is no way for the server to identify you. It just can't find out whether you're jpianoflorida or not, since the browser doesn't supply the session id or the cookie(s) required. If you logged off before, the login cache might not have been synchronized yet, so your user id is displayed as "online", but that's only a cosmetic thing and will change if you wait a bit longer. On the other hand, if you didn't log off then the server thinks you're still online and doesn't have anything to synchronize. There should be a timeout for this situation but I reckon it's quite long.
So to sum this up, the question should be whether you can post from a different machine or a different browser without logging in when you didn't log off on another one. This would be a security leak and should be handled by the administration. Anything else is due either a to performance optimization on the server or to the restrictions of the HTTP protocol, which doesn't allow the server to know that you closed the browser window without having logged off explicitely.
Topic: why am i still signed on?