Why have my last two completed games included a message that "game will not be rated." Whats up?

The most likely reason a game is not rated is because when your opponent sent out the challenge, they specifically chose the game to be "Unrated." The rating options when sending out a challenge are: Rated, 1/4 rated, and unrated.
 
When you receive the challenge notification, make sure you read it carefully as it will specify the rating type, including "Unrated." You can choose to accept or decline the challenge accordingly.