Hi there! On desktop you can press ESC, and click the folder icon - you will be able to view and transfer your savefiles directly! However this feature isn't in the web version at the moment.
Are you on the web or desktop version?
One option you can try is to test if pressing the manual 'quicksave' button in-game will have the savefile persist between sessions - on web the game uses cookies and something called indexedDB to store progress. If cookies or indexedDB are deleted, then there is no way to get the progress back. In that case, I can perhaps only recommend playing the desktop versions moving forward! But perhaps the above is worth a try!