I'm not being able to reproduce it. The save data is stored in %localappdata%\Pichon so it should work even if your account doesn't have administrator privileges.
One thing you can try is running the game with Steam open. There was a bug in an old version where the itch version was expecting the steam api to be available but if you are using version 19 that should be fixed.
If you are using the itchio sandbox try disabling it, though it shouldn't be an issue either.
If nothing works send an email to info@crimsonghostgames.com linking to this post and I'll send you a steam key to see if that works better.