Is something actually eating away at them or are they rotting? If they're rotting, I'd hazard to say poor polination.

Can't tell from the pic but yea poor pollination or slug damage. Do the leaves have lots of holes too?

Nope, no holes in the leaves. The slug thing is a possibility as I've seen some trails. I'm going to read up on the beer traps and set some of those. As far as pollination, I'm pretty sure that's not the issue. I've got bees in my squash all day! In fact, I can't get near them till almost sunset (actually got stung today). Could be rotting. I've discovered that I didn't plant deep enough and I'm going back and adding enough garden soil to try to get the plants back upright.

Just went out to the garden with a spotlight and it looks like it is slugs after all. First I saw a couple of cute little snails with their shells. Went inside and made up some soapy water in a bucket to drown them. Came back out and found 3 HUGE brown nasty slugs. The snails and slugs are all drowning quietly in my backyard. I had no idea they were that big or nasty looking!

You found the gardeners best kept secret - the flashlight. So many gardeners forget about looking after sundown, when so many things go on in the garden. Many spray for things they imagine it could be. Knowing what is doing the damage IS the biggest part of the solution.

btw- Insecticides will do nothing for slugs.

I've not had good luck with beer traps. What I do is two-fold - I keep an old pair of scissors (or shears) in the garden to cut'em in half - it works :-)

I've not had good luck using cold coffee - I do use ammonia and water (or coffee), in a spray bottle. Start with 10% or 20% ammonia if it doesn't make the slugs loose their grip on a vertical surface, add more ammonia until it does. You should see the slugs react immediately, then begin to dissolve (melt), then disappear completely.

If you have trouble bending over make a strong stream, kinda like a squirt gun. But I have found making a wider spray (or mist) often finds slugs I didn't even see.

I am sure you will find many more solutions but this is what I find works for me. To protect new sprouting seedlings, I use crushed egg shells and coarse sand, liberally sprinkled around the sprout. Supposedly to keep the slugs away. I am not convinced it is 100% effective so I also patrol with the ammonia spray until the plant can fend for itself.
Good Luck