So I found out what the issue is. It definitely is a power consumption issue on iOS. Once the phone drops beneath 20% background videos don't play on either Safari or Chrome. The Squarespace issue is that, if you dont have a backup mobile image selected then it should default to the colour background but it doesnt, it defaults to a still of the uploaded video with a playbutton that doesnt function.
The obvious 'fix' is to upload a backup mobile image and never rely on the background colour as a fall back.