I've been using AVAudioPlayer for several iOS apps and they all successfully playback after the screen locks until iOS6(or iOS5) on my iPad2, now they stop. Here is how I set it up, which used to work fine:
    // Registers this class as the delegate of the audio session.
    [[AVAudioSession sharedInstance] setDelegate: self];
    // Use this code instead to allow the app sound to continue to play when the screen is locked.
    [[AVAudioSession sharedInstance] setCategory: AVAudioSessionCategoryPlayback error: nil];
    UInt32 doSetProperty = 0;
    AudioSessionSetProperty ( kAudioSessionProperty_OverrideCategoryMixWithOthers,
                             sizeof (doSetProperty),
                             &doSetProperty
                             );
    [[UIApplication sharedApplication] beginReceivingRemoteControlEvents];
    // Registers the audio route change listener callback function
    AudioSessionAddPropertyListener (
                                     kAudioSessionProperty_AudioRouteChange,
                                     audioRouteChangeListenerCallback,
                                     (__bridge void *)self
                                     );
// Activates the audio session.
    NSError *activationError = nil;
    [[AVAudioSession sharedInstance] setActive: YES error: &activationError];
    // Instantiates the AVAudioPlayer object, initializing it with the sound
    AVAudioPlayer *newPlayer = [[AVAudioPlayer alloc] initWithContentsOfURL: medURL error: nil];
    self.appSoundPlayer = newPlayer;
    // "Preparing to play" attaches to the audio hardware and ensures that playback
    //      starts quickly when the user taps Play
    [appSoundPlayer prepareToPlay];
    [appSoundPlayer setVolume: 0.5];
    [appSoundPlayer setDelegate: self];
Note that I set the category to AVAudioSessionCategoryPlayback which was the fix that was recommended previously. This isn't working since I've upgraded to iOS6 -- also not working on iOS5 as it turns out!
Update: I found an answer that appears to be working based on this post: AVAudioPlayer stops playing on screen lock even though the category is AVAudioSessionCategoryPlayback
Basically I went into the Info page of the target and added a new key "Required background modes", to this I added a string type value "App plays audio". Now it makes it all the way through the track before turning the screen off completely.