Just released an update (2016.14) that now saves your scores so you can continue a game at a later time (on the same device).
Saving your score is automatic, you don't have to press any buttons. Your scores are saved locally on your device (nothing is saved to the "cloud") and restored when you revisit the game later or when you select refresh in your browser (use this trick to deal a new hand if you don't like the cards you were dealt).
Note that your scores are only saved after you complete a hand (when both player's hands and the crib have been counted). If you stop the game or close the web page before completing a hand your saved scores will not be updated.