Reinstalling the app might be worth a try. But you don't need to repurchase it. Just reinstall it. You can find the app under "My purchases" in the App Store.
But two other solutions would be:
a) repair the iTunes link for every song (open playlist manager, select a playlist for editing, select one of the red songs, tap on "Repair" and select the correct song in the iTunes browser.
b) delete the red songs and reimport them