I wasted a few development hours discovering this strange behaviour when binding to the IsChecked property of a RadioButton in WPF when using MVVM. You can read about the issue on the MSDN forum, but from my experience if you have a two way binding on the is IsChecked property of a RadioButton which is part of a group, then after you set the bound property in code a couple of times, the RadioButton loses it’s binding all together.

Here is my original code that kept losing it’s binding:

<ItemsControl ItemsSource="{Binding Elements}" Margin="0,10,0,10">
  <ItemsControl.ItemTemplate>
    <DataTemplate>
      <RadioButton Content="{Binding Key}"
        GroupName="{Binding RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type UserControl}}, Path=DataContext.Title}"
        IsChecked="{Binding Path=IsSelected}"
        Margin="0,5,0,5"/>
    </DataTemplate>
  </ItemsControl.ItemTemplate>
</ItemsControl>

There a couple of ways to solve this,

1. You can subclass the RadioButton
2. You could use OneWay binding on IsChecked to set the RadioButton state from code, then bind the Command property to a  Command when user clicks on the RadioButton.

   <ItemsControl ItemsSource="{Binding Elements}" Margin="0,10,0,10">
     <ItemsControl.ItemTemplate>
       <DataTemplate>
         <RadioButton Content="{Binding Key}"
           GroupName="{Binding RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type UserControl}}, Path=DataContext.Title}"
           IsChecked="{Binding Path=IsSelected, Mode=OneWay}"
           Command="{Binding IsSelectedCommand}"
           CommandParameter="{Binding}"
           Margin="0,5,0,5"/>
       </DataTemplate>
     </ItemsControl.ItemTemplate>
   </ItemsControl>

3. My preferred option: (as suggested by karliwatson) use a ListBox for the grouping and bind the ListBoxItem’s IsSelected property to your ViewModel, then bind the RadioButton’s IsChecked property to the list box item’s IsSelected property. Don’t set a group on the RadioButton.

   <ListBox ItemsSource="{Binding Elements}" Margin="0,10,0,10" BorderThickness="0" Background="Transparent">
     <ListBox.ItemContainerStyle>
       <Style TargetType="{x:Type ListBoxItem}">
         <Setter Property="IsSelected" Value="{Binding Path=IsSelected, Mode=TwoWay}" />
         <Setter Property="Template">
           <Setter.Value>
             <ControlTemplate TargetType="ListBoxItem">
               <ContentPresenter/>
             </ControlTemplate>
           </Setter.Value>
         </Setter>
       </Style>
     </ListBox.ItemContainerStyle>
     <ListBox.ItemTemplate>
       <DataTemplate>
           <RadioButton Content="{Binding Key}"
               IsChecked="{Binding Path=IsSelected, Mode=TwoWay, RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type ListBoxItem}}}"
               Margin="0,5,0,5"/>
       </DataTemplate>
     </ListBox.ItemTemplate>
   </ListBox>