Updated my test, it works 100% for web version of HTML export now, and persists within the session of installed HTML. Though I suppose local storage doesn't really work in "installed" HTML anyway (but if you found a way that'd be great :P). I work on Linux so I can't test Windows executable easily.
What do you mean when say "installed" HTML? sorry, didn't get it
Ah, I mean if you're running the itch client and click the "Install" button on a page with an HTML export. It just downloads the index.html and runs it when you click launch. I can't remember if local storage works in such a case.*
Now would be a good time for me to ask if there's an export for a Linux executable?
*Edit: Just tested, actually it does work. At least in Chrome browser, perhaps not in the itch browser. I'll test that now...
...aaand nope, it doesn't work in itch browser.
It's a pity, seems to itch client browser works like 'in private' mode
As for Linux exec export it's easy to implement I think, will try to add it in 0.0.11
The lack of persistent local data for HTML5 games in the itch app is a known issue: https://github.com/itchio/itch/issues/861
It derives from the fact that the game is served from a random http port every time it starts up (for example: http://localhost:23982) - it actually does save data, but the next time you start it, it won't load up the correct data.
The fix for that is probably to switch to a custom protocol (non-http), although that may cause other issues down the line. We're aware of the issue though, so there's hope!