unable to re download music from apps store. keep getting message that i need to re authorise

I am trying to redownload music from the itunes store.

The music downloads but will not play.

Instead I get a popup asking for my user id and password asking to authorise the computer.

i then get a computer authorised message but when i try to play the song, i get asked again for user id and password.

Can someone help please?

Many thanks,