If it was me, I might try to call the
private void App_Startup(object sender, StartupEventArgs e)
method again (as seen in App.xaml.cs) when the last slide is reached while the slideshow is actually running (in "play" mode).
But... that might get annoying, or confusing if someone manually clicks on the last slide and doesn't expect the source to refresh itself.
What you might want to do instead is add a button to the player (call it "refresh" or something, and add a little pop-up tooltip to explain what it does) that users can click themselves in order to refresh the slideshow/source.