Assuming you used the same iTunes account as you say, perhaps log out on ipad then back in again in Settings, Store (iOS 6 calls it iTunes&App stores). Then check you have the latest version of iReal b by checking in the App store for updates.
In iReal b, there will be an option in Hub, Store to restore your purchases.
If you are still having problems, backup your iPad iReal b songs (Hub, Utilities, Backup) or Send all your playlists and songs to yourself, uninstall iReal b then install again.
Also if you think there is a problem with your account, check with Apple.
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