Embedded video in header not showing in mobile browsers

I've added a video to the site according to the required dimensions. The video loads on desktop browsers, but not mobile browsers - tested on latest version of Safari & Firefox on latest iOS. The video will load and play in these browsers via a direct link to the file in Wordpress. So there's definitely a problem with the theme rendering. Hoping to go live with the site on Monday next week. So a speedy response to this would be much appreciated!!