Sometimes the installation of an in-app store items seems to get bogged down for whatever reason. I found that this procedure reliably takes care of the problem:
Ensure you have a stable Internet connection when running Music Maker, and open the program settings dialogue within the program (e.g. by pressing the "P" key in the Music Maker main screen). Find the "Clean up Store..." button in the "General options" tab and use it to reset the entire store. Follow the on-screen instructions. Please note that this will merely result in a local reset and clearing of downloaded store content. It will not result in you losing access to that content. The purchase status is stored in your account, and when logging into the store with your account, you would have access to your purchased content. So, when redownloading your content, this should now hopefully also result in the successful download and installation of the previously problematic item.