There is nothing we can do in the EMS side to kind of ‘push’ to the client application, in your case, web browsers. However, you can look at the client application configuration to see if it has a setting to try to reconnect and get the playlist.
What browsers are you using?
Try using VLC player and see if it can reconnect after the scenario you just described. If it can then i guess the VLC browser plugin can also work, assuming you can use the plugin.