IPhone 5 :: IOS 7.1.1 / Music App Asking For ITunes Verification

Recently (as in the past 2 or so days), when I am in the Music app and selecting a song to play, the little window to type in your iTunes password pops up and asks me to type in my iTunes password. I have already tried many things to remedy the situation. I've pressed cancel, and it goes away, but comes back randomly after a few minutes. I've put my password in [and yes, I put in the correct password] and the same thing happened.

I've signed out and signed back in, through both the Settings app AND through iTunes and the App Store on my device. I've turned it off and back on. I've plugged it in and synced it. I backed it up and did a full restore to that back up. No luck. The only thing that *seems* to work is just signing out and staying signed out. This is somewhat annoying, because now every time I want to buy a song, or update an App, I'll have to sign in, download it, and then sign out. Â

How I can fix this, without losing all of my data? I don't use iTunes Match or iCloud, so it couldn't be those things.