I'm using chrome on windows 10, and I think it may not be the game's fault, because I've gotten errors attached to localStorage on other things, so it may be my google account.
EDIT: I read the big block of text for iOS, (because I like reading, I know, I'm a nerd. What did you expect?) and I saw the bottom: "The only work-around for SIC-1 (...) is to manually export your save data...". Well then, I guess I'll do that!