Why do I get stars for daily awakening on some days and not on others?

Stars are earned on the daily awakening by guessing the words with the Red stars in them (on one of the letters). If you guess other words first then you don't progress.

To get the maximum 3 stars you have to find all the rods in the puzzle in the order that the stars appear. So only try to guess the word that seems to match the one marked by the star. When you get it right it will move to another word and so on. The more you get in the right order the more stars you earn.