Lately Jared Oswald has been posting some All Star Blitz episodes, and it led me to this question.
Why didn't they continue a puzzle into the next game? If time ran out, a player had the option to either guess the puzzle or totally end the game, meaning they start fresh the next show. It just seemed wasteful to get through the questions with the puzzle unsolved. My best guess is that they didn't want the players to try to figure out what the puzzle was between one show and the next.
Now an observation. I noticed that sometimes the stars will write someone's name on the answer cards for the Blitz Bonanza. I suppose that was their way to say "hello" to whomever they wanted.