I've seen many three years old threads about this, and looks like it is not yet fixed.
The issue is that the games status is saved in Javascript local storage, but after an update the game is stored on a different address, and all the data is lost.
Local storage is extremely easy to use, while any other solution, like using external API is quite annoying.
The only solution I see is to host the game in my own website, but this could be an issue for many itch users, not to mention loosing the visibility on this site.
Please make your CDN to save the games on fixed address, thanks.