How advanced are you? With a combobox, in effect, you have three components, the drop down menu, the button to drop it down, and the text area. Double click is probably not handled because of the three components, (which one fires the double click). It will probably require writing your own component class or sub class this component to handle a double click.
You may want to research overriding the WndProc method.
Easy solution, place a button right beside the combobox and use your doubleclick code on the buttons click event.
Sorry I can't be more help.