No there isn't any autosave right now. The only way to save the game is with the button.
I'm sorry that you lost your progress, I recommend you to take a break untill the next update. You can read more about it in the description of the game.
Actaully i've pressed save every few levels to be sure. Sometimes i've reloaded browser and game was loaded. And todays morning when browser restarted i saw again fresh game. Load doesn't help, all was lost. Maybe save was reseted due some patch and incompatibility between versions. I was playing on ipad - chrome, if it helps in any way.
Btw, game is great, i want to play again. I'm eagerly waiting for the patch to start again my path.