Ok, I'll try to explain more detail.
The basic concept for operator to be 'online' is to be able to chat with the visitors. So the operator becoming online only when he is entering the 'Visitors' page. And it's intended to be so.
After leaving the 'Visitors' page the operator will automatically become offline even if he is still logged in the system, since he is unable to chat with the visitors in this case. It will happen after the appropriate amount of time defined in the system settings (as it was written above).
If you want to become offline immediately, you can manually change the operator's status (it was written above too).
That's all. There are no other ways to change operator's status in Mibew Messenger 1.6.x.