1. Open the demo application >> Map >> Search example.
2. Enter some text and press Enter.
3. Move the mouse a little bit and you will notice the search box looses focus.

Workaround:  this.radMap1.MapElement.SearchBarElement.SearchTextBoxElement.TextBoxItem.LostFocus+=TextBoxItem_LostFocus;

        private void TextBoxItem_LostFocus(object sender, EventArgs e)
        {
            this.radMap1.MapElement.SearchBarElement.SearchTextBoxElement.TextBoxItem.TextBoxControl.Focus();
        }