iTunes can play most media files, including those purchased from the iTunes Music Store. However, sometimes iTunes seems to forget that you are authorized to play music that you have legally purchased. There are a number of reasons why this problem can occur, and each has a corresponding solution.
Authorize Computer via iTunes Music Account Menu: How to Fix iTunes Won't Let You Play Your Music
This guide will show you how to troubleshoot repeated authorization requests in iTunes.
Follow these steps in the order presented to resolve the authorization request and regain access to your music library.
Authorize the computer you're using. From the Account menu in the iTunes/Music app, select Authorizations > Authorize This Computer, then enter your Apple ID and password. This solution should resolve most media authorization issues.