How do I resolve 'This Mac isn't authorized' issue with authorized music on a specific Mac?

I have a couple of macs and have a problem with the 5th of 5 macs I'm allowed.

• click on song

• get message "this mac isn't authorized. Would you like to authorize it?

• Yup, I put in user name and password

• click on song

• Message "This mac isn't authorized...

• OK, as a test, I put same songs from another mac (same playlist; same songs) on a thumb drive and import into original mac.

• Music plays just fine

• What's the problem?

[Re-Titled by Moderator]