Watching the video in the Facebook app or in a browser? If in the Facebook app, uninstall Facebook, restart the phone and reinstall Facebook (from the Play Store, not from a backup). If it still happens, suspect the battery. (If you're watching the video in some other app when it happens, suspect that app - uninstall, restart, reinstall.)
Also watch a few videos in the Youtube app. If it happens there too, there's a problem with the phone or the battery.