Do you have any bees or other pollinating insects in your yard?

You might try hand-pollinating your patty pans and see if that changes the pattern.

Let me guess, they just recently started making flowers at all. It's normal. Just be patient.

The one on the left is male,
the one on the right is female:

Female blossom:
{{gwi:49713}}

bobbi socal, I may have misread your post the first time. Are you saying the female flowers are dropping off half-formed, before they even start to open?

If so, it certainly doesn't sound like a pollination problem. Very strange.

Both plants have already successfully produced fruit. So we have had female and male blossoms running amuck. The bees are buzzing, the ants are anting....we got us really great polinators!

But then suddenly ----- All new female flowers are not getting past about 1 & 1/2" (inches)tall before they start to shrivel and fall off. So they don't ever get close to opening to be polinated.

Does that explain the trouble better?

What are your temperatures like? Last year most of my female squash blossoms dropped off the plant unopened once the temps got high.

Or maybe your plants are putting all their energies into ripening the fruits they've already set.

Could it be that they feel that already have enough to support the fruit growing on their vines without adding more. Probably their own form of birth control. I am of the opinion that there is something in plants that govern their actions based on their environmental circumstances. I have seen trees shed excess leaves after a drought sets in, Same thing with some fruit trees.
Just a thought.
Bill P.