Authorize computer message for iTunes in iMovie HD

I have purchased songs off of iTunes(latest version) and while making a iMovie and placing them on my timeline I get the, "This computer is not authorized to play "such in such a song.m4p". It will play in iTunes and initially in iMovie and when I click on the Audio section in iMovie and drag it onto the timeline it played for a bit. It will even let me edit it then the message pops up. So I follow the onscreen prompts to open iTunes and authorize it. I type in my Apple ID and password and hit enter. It states Machine authorization successful.You have authorized a total of 3 machines out of your available 5. So I go back to iMovie in the Media/audio section and click on the songs I have downloaded and its groundhog day all over again. I have authorized a myriad of times and even deauthorized (it still says 3 out of 5 machines). I have deleted the sound clips off my iMovie timeline, came back later and played them again and every once in awhile they play for a few minutes then the "This computer is not......" message pops up again and again and again...! Any suggestions????