I see visitor in "Browsing" status even though he/she has already left my site
LiveHelpNow does not keep permanent connection with your visitors so it has no way of knowing the exact time of departure of your visitors.
The operator panel will set the visitor's status to "browsing" immediately after the visitor views any page of your site where LiveHelpNow code is installed. If the visitor had left the site or simply became idle for 3+ minutes his/her status will be set as "departed", should the visitor navigate to the new page of your site his/her status will be reset to "browsing" again until he/she will become idle again for 3+ minutes.