Water keeps draining out of the overflow

Unfortunately on many rv's the overflow is plumbed in such a way that once it starts to drain for any reason such as sloshing as you go around a corner, it creates a vacuum and can empty the entire tank. For now your best bet is to plug the drain but don't forget to remove the plug when filling the tank. The correct fix is to find the overflow line and loop it upwards above the tank then down.