DataTemplate disappears when moving items in ObservableCollection - wpf

Question

I have a CellTemplate for a column in a ListView. The CellTemplate contains a ComboBox which has an ItemTemplate. Both ItemsSource and SelectedItem is bound to another ViewModel.
The ListView is bound to an ObservableCollection on a ViewModel. Above the ListView there is a toolbar with the buttons to move the selected item up and down. I buttons a bound to and ICommand which will make a Move on the ObservableCollection.
The view is updated fine, but the selected item in the ComboBox is not using the DataTemplate and is just showing the type name.
I found out that everything is working fine if IsEditable = false, but I need this to be true.
I have created a small project that verifies the problem. Perhaps this is an issue in WPF.
Here is XAML:
<Window x:Class="WpfApplication3.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" xmlns:WpfApplication3="clr-namespace:WpfApplication3"
Title="MainWindow" Height="350" Width="525">
<Window.Resources>
<DataTemplate DataType="{x:Type WpfApplication3:Item}">
<TextBlock Text="{Binding Name}"/>
</DataTemplate>
<DataTemplate x:Key="cellTemplate">
<ComboBox ItemsSource="{Binding Items}" SelectedItem="{Binding SelectedItem}" Width="100" IsEditable="true" TextSearch.TextPath="Name"/>
</DataTemplate>
</Window.Resources>
<Grid>
<StackPanel>
<ToolBar>
<Button Content="Add" Command="{Binding AddItemCommand}"/>
<Button Content="Up" Command="{Binding MoveItemUpCommand}" CommandParameter="{Binding ElementName=listView, Path=SelectedItem}"/>
<Button Content="Down" Command="{Binding MoveItemDownCommand}" CommandParameter="{Binding ElementName=listView, Path=SelectedItem}"/>
</ToolBar>
<ListView x:Name="listView" ItemsSource="{Binding Collection}">
<ListView.View>
<GridView>
<GridViewColumn Header="Name" CellTemplate="{StaticResource cellTemplate}"/>
</GridView>
</ListView.View>
</ListView>
</StackPanel>
</Grid>
public partial class MainWindow : Window
{
public MainWindow()
{
InitializeComponent();
DataContext = new ViewModel();
}
}
public class ViewModel
{
public ICommand AddItemCommand { get; private set; }
public ICommand MoveItemUpCommand { get; private set; }
public ICommand MoveItemDownCommand { get; private set; }
public ObservableCollection<Row> Collection { get; set; }
public ViewModel()
{
Collection = new ObservableCollection<Row>();
AddItemCommand = new RelayCommand(AddItem);
MoveItemUpCommand = new RelayCommand<Row>(MoveItemUp, CanMoveItemUp);
MoveItemDownCommand = new RelayCommand<Row>(MoveItemDown, CanMoveItemDown);
}
private bool CanMoveItemDown(Row arg)
{
if (arg == null)
return false;
return Collection.Last() != arg;
}
private void MoveItemDown(Row obj)
{
var index = Collection.IndexOf(obj);
Collection.Move(index, index + 1);
}
private bool CanMoveItemUp(Row arg)
{
if (arg == null)
return false;
return Collection.First() != arg;
}
private void MoveItemUp(Row row)
{
var index = Collection.IndexOf(row);
Collection.Move(index, index - 1);
}
private void AddItem()
{
Collection.Add(new Row());
}
}
public class Row
{
public Row()
{
Items = new List<Item> { new Item { Name = "Test1" }, new Item { Name = "Test2" } };
}
public List<Item> Items { get; set; }
public Item SelectedItem { get; set; }
}
public class Item
{
public string Name { get; set; }
public int Order { get; set; }
}