Hmm! Are you playing through the website? The save files should be saved locally in your browsers cache, so it might be that you have a super aggressive 'delete cache and cookies' set up where it wipes the browser when you navigate away.
An alternative workaround. There's an option at the bottom. 'Save/Load from disc'. This will allow you to create an actual file on your computer that contains the save. Slightly more cumbersome than having the saves just in the game, but it should allow you to keep them where you want and ensure they're available even if your browser is wiped and clean.