Zuchinni, as with other cucurbits, will produce both male and female
flowers. The males are on a stalk and the females have a swollen embryo fruit at the base of the
flower and no stalk. Maybe you are not getting full pollination on all the females. This usually results in the unfertilised embryo fruit going yellow and just dying and dropping off. Is this what's happening?
Insects will normally do the pollination for you. That's OK. Just take a male
flower, remove the petals and brush it on the female stamen. (Or is that stigma?) Anyway, the innards of the female
flower. This is best done each morning when the
flowers are fully open. You can also eat the
flowers. They are great dipped in batter and fried or just eaten fresh or as a side dressing to a salad. Make sure there isn't a bee in there though;)