I am experiencing same exact issue.
Note: on Flash Builder burrito, dropdownlist control works fine, same exact code on FB 4.5 having this issue i.e DropDownList get created fine,
when user tap on it, it display the items in list, BUT when you try to select any item, the list collaps to its original state.
Another interesting fact: only way I was able to select an item in list is to use hardware 4-way keys in my Motrola Droid. Tapping on the DropDownList just dont seems to work.
here is a sample code (that do not work properly in FB 4.5)
I have the same problem , Dropdownlist used to work fine in BURRITO it select the item and keeps it using mouse during debug or touch on the device ,, Since i unintalled Burrito and installed 4.5 THE component function exactly as anixan decribes it the selection alwayes blank using mouse or touch on device but during debug if i use arrow keys it works , it seems that there is a bug or problem in the Release of Flash Builder 4.5. I tried searching google for dayes for answer but no luck.