If you define a separate focus scope in XAML to maintain the selection (see StackPanel below) and you set the focus in the TextBox once (in this case when the Window opens using FocusManager.FocusedElement) then you should see your selection change programatically.
Here is some sample code to get you started:
<Window x:Class="RichTextFont2.Views.MainView"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Main Window"
Height="400" Width="400"
FocusManager.FocusedElement="{Binding ElementName=myTextBox}"
FontSize="20">
<DockPanel>
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="60"/>
<RowDefinition/>
</Grid.RowDefinitions>
<TextBox x:Name="myTextBox"
Grid.Row="0"
Text="Text that does not loose selection."
TextWrapping="Wrap"
VerticalScrollBarVisibility="Auto">
</TextBox>
<StackPanel Grid.Row="1" FocusManager.IsFocusScope="True">
<Button Content="Select Text" Click="Button_Click_MoveTextBox"/>
</StackPanel>
</Grid>
</DockPanel>
</Window>
Here is some code to handle the button click event:
private void Button_Click_MoveTextBox(object sender, RoutedEventArgs e)
{
if (myTextBox.SelectionStart >= myTextBox.Text.Length)
{
myTextBox.SelectionStart = 0;
}
else
{
myTextBox.SelectionStart += 9;
}
myTextBox.SelectionLength = 6;
myTextBox.LineDown();
}