In scenarios like this one, the control should be populated only if the drop down is not open whenever the GotFocus event is fired. Please use the following code snippet as a reference:

private void RadAutoCompleteBox_GotFocus(object sender, RoutedEventArgs e)
{
    var autoCompleteBox = sender as RadAutoCompleteBox;
    if (!autoCompleteBox.IsDropDownOpen)
    {
        autoCompleteBox.Populate(autoCompleteBox.SearchText);
    }
}

Regards,
Kalin