A couple of years ago I thought I was probably the only person that could not grow zucchinis. In disappointment I would see how what I thought were baby zucchinis would start forming at the base of the plant, only to wither and rot in a couple of days. After researching the problem I came to the conclusion that we probably had not enough bees in our property to fertilize the flowers.
Zucchinis produce two kinds of flowers, the female flower usually grows close to the base of the plant and is attached to the ovary (a zucchini looking organ). The male flower, on the other hand usually grows on a tall stem closer to the top of the plant, and away from the fruit bearing flower. Since the sexual organs of the plant are held in separate flowers, the pollen must reach the female organ and fertilize the flower for the zucchini to actually form, mature and grow. If the garden does not have sufficient bees or other pollinating insects to move the pollen from one flower to the other one must do the work.
The zucchini flowers open up early in the morning, by 5:30-6:00 they are in full bloom. I go out in the garden early before the flowers wilt, and with a q-tip I swab the stamens to collect pollen that I then transfer to the female organ by gently touching them with it. By doing this I have been able to obtain a steady production of zucchinis throughout the summer.