Assuming your custom ComboBox inherits from the WinForms native ComboBox:
Putting this in the SelectedIndexChanged EventHandler:
if(! comboBox1.DroppedDown) comboBox1.DroppedDown = true;
Will force the DropDown to stay dropped until you either click in the selection text display area of the ComboBox, or you click outside the ComboBox so that the ComboBox loses Focus.
Are you doing something that implements multi-selection ?