Usually then you go offline or online visitors has to refresh page to see new widget status. Since 2.08v it's possible to make status changes visible without required pageview.

You just have to go to "Configuration => Live Help configuration => Chat configuration => Misc => Interval between chat status checks in seconds, 0 disabled." I suggest to set there value 300 it will be status check every 5 minits. Usually if you have not changed default configuration it's foreseen that operator status changes if his last activity was 5 minits ago.

In any case if you want to be more realtime you can reduce this time. But have in mind that every time status check is performaned there is involvment of request to server.