Sorry to hear your saves are being lost! If you're on Windows, MacOS or Linux, you could try downloading the game via the official itch.io app. That may be able to preserve your saves & will keep the local copy updated.
If you're playing on a smartphone, then you could try a different browser, or check for browser settings that remove your history or clear/block cookies. Playing in an incognito/private window will also delete your saves. If nothing else works, you could try what shogungari suggested & export/import your data via the Extras main menu option.
I'll look at options to improve this in a future update.