One member assumed the "online" status was live but that is not the case. The "online" status for the forum is based on page loads as it is on other browser based applications elsewhere. I have it set at 5 minutes, if you load a page you're "online". Every time you load another page in that 5 minute window the 5 minute countdown gets reset. If you don't load another page in 5 minutes you'll go "offline".
In other words the "online" really means the member viewed a page in the last 5 minutes.
The auto login feature has no part in this and is separate altogether, if you use the auto login feature you'll still go "offline" after 5 minutes.
One thing to note is some browser based applications are using AJAX that will continually communicate with the server for a true "live" list. These are pretty common in chat based applications commonly referred to as "shoutboxes". I'm currently not using anything like that.