I guess its not with respect to QTP11/10, its the technology that is used which QTP will not be able to identify it correctly if the proper add-in is not available.
Like if you see any app with Ajax used, you would face a similar issue where the links, dropdowns etc would be identified as WebElements.
can you post the screenshot spying both the list box and the arrow associated to it.
Also can you please try clicking on the arrow, put a wait for a second and then click the appropriate item which you would like to.
Terry try something crude like placing a Wait(10) prior to the statement that is intermittently failing. Then iterate over that line a number of times, if each functions correctly then it is probably an inconsistent rendering time.
That's the easy bit, post your results and then lets all have another crack at the route cause.