In Facebook you have to tell him that if the stream loses connection it mustn't terminate the streaming, because it has that as default option (I don't remember exactly how to do it, it's somewhere in the streaming option). OBS should reconnect by default, you can verify it in "settings" -> "advanced" -> "automatically reconnect" and if you want you can change how much time it waits to try a reconnection and how many attempts he makes to reconnect