Nvm, sorta jumped the gun with the question. Haven't looked at the source, but by inspection it seems the ComboBox's content view covers the underlying mouse area that is used to access the menu.
Setting the rightPadding and leftPadding of the ComboBox appropriately uncovers the clickable region on that side of the ComboBox, so, for example, setting rightPadding to 10 gives a 10px wide clickable region on the right, and likewise for the left.