If you experiment messages lost during the live chat session despite the fact that messages are stored in the database and visible in the backend list, the problem could be related to several reasons.
If you are keeping opened multiple browser tabs to the website running the chat appliction, that could be the problem. In such case to avoid to lose messages between different tabs keeping all tabs synced, you have to enable the 'Multitabs messages download' parameter. Otherwise you have to take care to always keep opened only one single tab running the chat application.
Another reason why messages are lost and not received could be due to the server resources and bandwidth. If you have poor server resources and several concurrent users, there could be not enough resources to provide a stable data stream to all connected users. In such case you can try to reduce the 'Server load' and increase the 'Max inactivity time to strip out users' using settings below and check if that helps:
Finally the problem could be completely outside the scope of Joomla! and JChatSocial, indeed if users have network connectivity issues they might intermittently lose the connection to the server and the data stream thus missing to receive messages. If this is the case, there is nothing to do on the app side, users must take care to use a reliable internet connection. Keep in mind that there are even mobile devices and browsers that in certain cases suspend the network connectivity to save bandwidth.