How do I get a final authorization for music I have purchased and authorized for my three computers?

Many tunes I have purchased are not "authorized" on my computer. After entering my username and password, I receive a text box to the equivalent of "this was previously authorized and is now authorized for this computer. You have authorized three of the five allowed." Yet when I try to play the same song, I get the "this song is unauthorized on this computer." Repeatedly. Grrr.