We make the assumption that, whether those gourds break or not, depends entirely on the height from which they fall. In particular, it does not matter how many previous descents the vegetable endured, as long as it is still intact. However, since this is not a physics or botanics problem, we cannot make any assumptions as to the toughness of those culinary fruits ;)
What is the minimum number of droppings needed to identify the crush-critical height?
From which floor should you throw your first squash vegetable?
Note: See Egg drop for a similar, but slightly easier challenge.