Ive seen messages all over google pretty much about:

My computer says it is not authorized to play certain songs. When I try to authorize it, it takes my password XXXXX however, does not actually authorize it.

and so on…

Well, today (2/5/12) I bought an album Wester – Danger Music, everything downloaded and added to my iTunes. 1 Problem thou, one of the songs would not play, kept getting the error message iTunes – “not authorized to play on this computer”

I tried the options from (http://support.apple.com/kb/TS1389) iTunes repeatedly prompts to authorize computer to play iTunes Store purchases

Those did not work for me, so what I did to fix this issue was very simple.

1. Delete the song in iTunes to remove from your library and hard drive

2. Open the iTunes Store

3. Make sure you are signed in with the same account used for the original purchase.

4. Tap Purchased from the bottom navigation bar in the Features category.

5. From the Purchased tab, tap the artist name for the content you intend to download again.

6. Once you’ve located the music you are looking for, tap the download button.

(If you want to download all songs from an album that you’ve purchased, click on the button to swith to the “Album” view.)

Hope your issue is Fixed!

Thats IT!! I was stuck trying to figure out a fix for an hour, and finally figured this out.

Any questions please don’t hesitate to ask.