This game does not auto-save, and game overs make you reload a save, so be sure to save regularly. If you forget to save for a long time and lose progress, the Chapters function will at least let you start from the beginning of each chapter/part.
Saves for the browser version are stored in your browser’s Local Storage. They should persist across sessions. However, they may get erased if you clear your browser history in a way that wipes Local Storage, or use some sort of incognito mode or private browsing that doesn’t save Local Storage.