How to force a WPF binding to refresh?

You can use binding expressions:

private void ComboBox_Loaded(object sender, RoutedEventArgs e)
{
    ((ComboBox)sender).GetBindingExpression(ComboBox.ItemsSourceProperty)
                      .UpdateTarget();
}

But as Blindmeis noted you can also fire change notifications, further if your collection implements INotifyCollectionChanged (for example implemented in the ObservableCollection<T>) it will synchronize so you do not need to do any of this.