It happened to me at first too, you can actually export the save and import it later at the extra button in the main menu, it will save in your files on the pc so you shouldn't lose it like that.
Are you playing in an incognito/private browser tab? That can sometimes interfere with your browser's local storage. The next update (which I'm very close to finishing now) changes saves to use IndexedDB instead, which might help.
The issue is that, after saving, if I leave to the main menu, everything is immediately gone, so I have no ability to export or import. If there was a export button inside the game settings then this would work.
