Aurthorizing Computer

I purchase several albums per week. Sometimes, after a purchase, I can't play all the songs due to the "Aurthorize this Computer" prompt. When I re-aurthorize the computer, it seems to go through but when I go to play the song/songs, I get the same prompt again. I will have to quit purchasing music off of Itunes if I can't play them. What am I doing wrong?