WPF DoDragDrop causes control animation to halt

Question

Here's the scenario (simplified): I have a control (let's say, a Rectangle) on the Window. I hooked the MouseMove event to make it initiate a drag&drop. Then in the MouseDown event I let it animate, moving 50 pixels to the right. However, when I hold my mouse down on the Rectangle, the control moves about one pixel, and then pauses. Only when I move my mouse will the animation continue. Does anyone know why and how to solve this? Thanks a lot!!

Here's the source code to reproduce this problem:

public partial class Window1 : Window
{
    public Window1()
    {
        InitializeComponent();
    }

    private void rectangle1_MouseMove(object sender, MouseEventArgs e)
    {
        if (e.LeftButton == MouseButtonState.Pressed)
        {
            DragDrop.DoDragDrop(this, new DataObject(), DragDropEffects.Copy);
        }
    }

    private void rectangle1_MouseLeftButtonDown(object sender, MouseButtonEventArgs e)
    {
        ThicknessAnimation animation = new ThicknessAnimation();
        Thickness t = rectangle1.Margin;
        t.Left += 50;
        animation.To = t;
        animation.Duration = new Duration(TimeSpan.FromSeconds(0.25));
        rectangle1.BeginAnimation(Rectangle.MarginProperty, animation);
    }
}

In case you want Window1.xaml:

<Window x:Class="DragDropHaltingTest.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Grid>
    <Rectangle Margin="12,12,0,0" Name="rectangle1" Stroke="Black" Fill="Blue" Height="29" HorizontalAlignment="Left" VerticalAlignment="Top" Width="31" MouseMove="rectangle1_MouseMove" MouseLeftButtonDown="rectangle1_MouseLeftButtonDown" />
</Grid>