I believe a warning should appear when starting the game on web iPhone warning about this and to save often.
But basically, the iOS doesn't handle web games very well.
And when doing things (like loading assets), if it ever feels like it has loaded too much stuff on that session, it force refreshes the browser tab.
This is something that only happens on iPhone/iPad and since it's a deliberate feature done by Apple, from what I was able to investigate there isn't anything I can really do about it, unfortunately.
So if you can't find another device to play on, I can only recommend saving as often as you can.

