I had this problem last year, and finally got to the bottom of it.
If the fruit doesn't get pollinated, it aborts. This is what is described.
Plant more zucchini now! Come back when you've done that, and I'll explain.
OK good, here's the deal.
There are two kinds of flowers: male and female. You gotta get a pollinator to visit a male flower, then a female flower, but this is not happening.
Most assume it is a lack of pollinators, and often this is the case.
However, what I discovered last year is that I had no male flowers. Beautiful healthy plants with plenty of female flowers. But not even one lone soldier to take care of the girls.
It turns out that as the plants get older, they start producing only female flowers. So you need young plants all season long.
That's why I asked you to go out and plant more zucchini. And why I will not be thinning them down to just two plants this year, and come to think of it, I'm going to go poke a couple more seeds in right now myself.