I was surprised to see that the XAML media element did not have a loop property built into it. Surely having a clip loop is basic functionality? In any case I came up with a JavaScript solution that seemed much simpler to implement than the pure XAML solution offered on the MSDN website. 

JavaScript Solution

    handleLoad: function(control, userContext, rootElement)
    {
        this.control = control;

        //  Get a reference to your media element (mine is called "MainMovie")         
        this.movie = control.content.findName("MainMovie");
        // Add an Event Listener for the "MediaEnded" Event
       this.movie.addEventListener("MediaEnded", Silverlight.createDelegate(this,this.movieMediaEnded));
    },

    //When the end of the movie is reached, return the movie to the start and play it again
    movieMediaEnded: function(sender, eventArgs)
    {
        sender.Position = "00:00:00";
        sender.play();
    }

See my solution in action at The Daily Prophet Online.

MSDN's Pure XAML Solution

<Page xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"

xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" >

<StackPanel>

<!-- The MediaElement control plays the sound. -->

<MediaElement Name="myMediaElement" >

<MediaElement.Triggers>

<EventTrigger RoutedEvent="MediaElement.Loaded">

<EventTrigger.Actions>

<BeginStoryboard>

<Storyboard>

<!-- The MediaTimeline has a RepeatBehavior="Forever" which makes the media play

over and over indefinitely.-->

<MediaTimeline Source="media\tada.wav" Storyboard.TargetName="myMediaElement"

RepeatBehavior="Forever" />

</Storyboard>

</BeginStoryboard>

</EventTrigger.Actions>

</EventTrigger>

</MediaElement.Triggers>

</MediaElement>

</StackPanel>

</Page>