Stop TabControl from recreating its children

By default, the TabControl shares a panel to render it’s content. To do what you want (and many other WPF developers), you need to extend TabControl like so:

TabControlEx.cs

[TemplatePart(Name = "PART_ItemsHolder", Type = typeof(Panel))]
public class TabControlEx : TabControl
{
    private Panel ItemsHolderPanel = null;

    public TabControlEx()
        : base()
    {
        // This is necessary so that we get the initial databound selected item
        ItemContainerGenerator.StatusChanged += ItemContainerGenerator_StatusChanged;
    }

    /// <summary>
    /// If containers are done, generate the selected item
    /// </summary>
    /// <param name="sender"></param>
    /// <param name="e"></param>
    private void ItemContainerGenerator_StatusChanged(object sender, EventArgs e)
    {
        if (this.ItemContainerGenerator.Status == GeneratorStatus.ContainersGenerated)
        {
            this.ItemContainerGenerator.StatusChanged -= ItemContainerGenerator_StatusChanged;
            UpdateSelectedItem();
        }
    }

    /// <summary>
    /// Get the ItemsHolder and generate any children
    /// </summary>
    public override void OnApplyTemplate()
    {
        base.OnApplyTemplate();
        ItemsHolderPanel = GetTemplateChild("PART_ItemsHolder") as Panel;
        UpdateSelectedItem();
    }

    /// <summary>
    /// When the items change we remove any generated panel children and add any new ones as necessary
    /// </summary>
    /// <param name="e"></param>
    protected override void OnItemsChanged(NotifyCollectionChangedEventArgs e)
    {
        base.OnItemsChanged(e);

        if (ItemsHolderPanel == null)
            return;

        switch (e.Action)
        {
            case NotifyCollectionChangedAction.Reset:
                ItemsHolderPanel.Children.Clear();
                break;

            case NotifyCollectionChangedAction.Add:
            case NotifyCollectionChangedAction.Remove:
                if (e.OldItems != null)
                {
                    foreach (var item in e.OldItems)
                    {
                        ContentPresenter cp = FindChildContentPresenter(item);
                        if (cp != null)
                            ItemsHolderPanel.Children.Remove(cp);
                    }
                }

                // Don't do anything with new items because we don't want to
                // create visuals that aren't being shown

                UpdateSelectedItem();
                break;

            case NotifyCollectionChangedAction.Replace:
                throw new NotImplementedException("Replace not implemented yet");
        }
    }

    protected override void OnSelectionChanged(SelectionChangedEventArgs e)
    {
        base.OnSelectionChanged(e);
        UpdateSelectedItem();
    }

    private void UpdateSelectedItem()
    {
        if (ItemsHolderPanel == null)
            return;

        // Generate a ContentPresenter if necessary
        TabItem item = GetSelectedTabItem();
        if (item != null)
            CreateChildContentPresenter(item);

        // show the right child
        foreach (ContentPresenter child in ItemsHolderPanel.Children)
            child.Visibility = ((child.Tag as TabItem).IsSelected) ? Visibility.Visible : Visibility.Collapsed;
    }

    private ContentPresenter CreateChildContentPresenter(object item)
    {
        if (item == null)
            return null;

        ContentPresenter cp = FindChildContentPresenter(item);

        if (cp != null)
            return cp;

        // the actual child to be added.  cp.Tag is a reference to the TabItem
        cp = new ContentPresenter();
        cp.Content = (item is TabItem) ? (item as TabItem).Content : item;
        cp.ContentTemplate = this.SelectedContentTemplate;
        cp.ContentTemplateSelector = this.SelectedContentTemplateSelector;
        cp.ContentStringFormat = this.SelectedContentStringFormat;
        cp.Visibility = Visibility.Collapsed;
        cp.Tag = (item is TabItem) ? item : (this.ItemContainerGenerator.ContainerFromItem(item));
        ItemsHolderPanel.Children.Add(cp);
        return cp;
    }

    private ContentPresenter FindChildContentPresenter(object data)
    {
        if (data is TabItem)
            data = (data as TabItem).Content;

        if (data == null)
            return null;

        if (ItemsHolderPanel == null)
            return null;

        foreach (ContentPresenter cp in ItemsHolderPanel.Children)
        {
            if (cp.Content == data)
                return cp;
        }

        return null;
    }

    protected TabItem GetSelectedTabItem()
    {
        object selectedItem = base.SelectedItem;
        if (selectedItem == null)
            return null;

        TabItem item = selectedItem as TabItem;
        if (item == null)
            item = base.ItemContainerGenerator.ContainerFromIndex(base.SelectedIndex) as TabItem;

        return item;
    }
}

XAML

<Style TargetType="{x:Type controls:TabControlEx}">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type TabControl}">
                <Grid Background="{TemplateBinding Background}" ClipToBounds="True" KeyboardNavigation.TabNavigation="Local" SnapsToDevicePixels="True">
                    <Grid.ColumnDefinitions>
                        <ColumnDefinition x:Name="ColumnDefinition0" />
                        <ColumnDefinition x:Name="ColumnDefinition1" Width="0" />
                    </Grid.ColumnDefinitions>
                    <Grid.RowDefinitions>
                        <RowDefinition x:Name="RowDefinition0" Height="Auto" />
                        <RowDefinition x:Name="RowDefinition1" Height="*" />
                    </Grid.RowDefinitions>
                    <DockPanel Margin="2,2,0,0" LastChildFill="False">
                        <TabPanel x:Name="HeaderPanel" Margin="0,0,0,-1" VerticalAlignment="Bottom" Panel.ZIndex="1" DockPanel.Dock="Right"
                                  IsItemsHost="True" KeyboardNavigation.TabIndex="1" />
                    </DockPanel>
                    <Border x:Name="ContentPanel" Grid.Row="1" Grid.Column="0"
                            Background="{TemplateBinding Background}"
                            BorderBrush="{TemplateBinding BorderBrush}"
                            BorderThickness="{TemplateBinding BorderThickness}"
                            KeyboardNavigation.DirectionalNavigation="Contained" KeyboardNavigation.TabIndex="2" KeyboardNavigation.TabNavigation="Local">
                        <Grid x:Name="PART_ItemsHolder" Margin="{TemplateBinding Padding}" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}" />
                    </Border>
                </Grid>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

Note: I did not come up with this solution. It has been shared in programming forums for several years and believe that it is in now one of those WPF recipes books. The oldest or original source for I believe was PluralSight .NET blog post and this answer on StackOverflow.

HTH,