If you have deleted the app or just deleted a song you can restore your purchases by tapping the "Restore Purchases" button.
Now select the songs you want to restore (note that you need to have downloaded the song at some time, in order to restore it).
And tap the "Restore" button on the top right corner of the dialog box.
Enter your App Store account password to confirm the restoration of your purchases.
Restoration of your purchases is now complete!
Just wait for the necessary files to download.