You can use local storage to save data. We currently have an issue where uploading a new build of your game changes the path it lives on, so you might lose your storage depending on how you've saved it.
just out of curiousity is this still an issue?
I'm looking at making an HTML5 game, while I'm alpha/beta testing I'll probably be releasing updates fairly regularly. I don't really want testers to loose their progress for minor changes.
Maybe you can provide a backup feature, just in case they use another computer, or clear the browser data by accident. For example, open a text box and show the saved string and allow the user to copy them. Or download as a file that can be imported later.
Also localStorage is like cookie, so if you store something on a.itch.io/game1, you can't acces it from b.itch.io, but you can access it from a.itch.io/game2. It depends on the domain name of your linked game.