Change input scope for textbox programmatically multiple times on Windows Phone 8.1 app

Question

I am trying to change the input scope for a textbox in Windows Phone 8.1 app programmatically at runtime, but the change only works the first time.

I have this xaml page:

<Page
    x:Class="InputScopeTest.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:InputScopeTest"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    Background="{ThemeResource ApplicationPageBackgroundThemeBrush}">

    <Grid>
        <TextBox x:Name="textBox" HorizontalAlignment="Left" Margin="53,117,0,0" TextWrapping="Wrap" Text="TextBox" VerticalAlignment="Top" Width="302"/>
        <Button x:Name="buttonAlpha" Content="Alpha" HorizontalAlignment="Left" Margin="53,229,0,0" VerticalAlignment="Top" Click="buttonAlpha_Click"/>
        <Button x:Name="buttonNumeric" Content="Numeric" HorizontalAlignment="Left" Margin="246,229,0,0" VerticalAlignment="Top" Click="buttonNumeric_Click"/>
    </Grid>
</Page>

And this .cs page:

using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;
using Windows.UI.Xaml.Input;
using Windows.UI.Xaml.Navigation;

namespace InputScopeTest
{
    public sealed partial class MainPage : Page
    {
        public MainPage()
        {
            this.InitializeComponent();

            this.NavigationCacheMode = NavigationCacheMode.Required;
        }

        protected override void OnNavigatedTo(NavigationEventArgs e)
        {
        }

        private void buttonAlpha_Click(object sender, RoutedEventArgs e)
        {
            InputScope scope = new InputScope();
            InputScopeName name = new InputScopeName();

            name.NameValue = InputScopeNameValue.AlphanumericFullWidth;
            scope.Names.Add(name);

            textBox.InputScope = scope;
        }

        private void buttonNumeric_Click(object sender, RoutedEventArgs e)
        {
            InputScope scope = new InputScope();
            InputScopeName name = new InputScopeName();

            name.NameValue = InputScopeNameValue.Number;
            scope.Names.Add(name);

            textBox.InputScope = scope;
        }
    }
}

On both the emulator and a windows phone 8.1 device the input scope for the textbox changes correctly only the first time you tap one of the buttons. For example if I tap the "Numeric" button first, the input scope changes to a numeric keyboard correctly. But if I then tap the "Alpha" button, the input scope does not change to an alphanumeric keyboard as it should.

The above code is taken from MSDN and it looks that it only works if you change the scope the first time. The second time the change is ignored.

Am I doing something wrong? Is there another way to set the input scope for a textbox programmatically multiple times?