How long have they been flowering? If less than three weeks, then this is normal.

I have the same problem, but it is ongoing, well after 3 weeks. My plant looks very healthy, but the baby squash are rotting & falling off. What can I do to avoid spoiling the small squashes on the vine? My vine is trellised and the fruit well supported.

Does it need for each flower to be fertilized by hand or what?

Probably, squash are insect pollinated. If insects such as bees are scarce, you need to intervene with hand pollination.

It sounds like they don't get pollinated.
Sure fire cucurbita pollinators are honey and bumble bees.
They hang around here a lot, especially bumble bees.
If you don't see them around your garden then you have to do it yourself.Actually it is very easy to do. The only difficulty that I have , once in a while pollinating my night-flowering gourds,is reaching them on the trellis.
My success rate is better than 90%.

Hand pollinating squash is pretty simple too. And fruit that grow a couple inches and then rot and fall off- that is definitely lack of pollination.

If you aren't sure how to hand pollinate, get a small paintbrush (like one from a kid's watercolor set, nothing too big) or a qtip. Go out when the flowers are open, first brush your instrument on the part of the male flower that's got all the pollen on it. (The end of your qtip or paintbrush will get yellow pollen all over it.) Then go over to the female flowers (these are the ones with the small squash behind the flower), brush the pollen on the parts within the female flower. Within days, you should start to see a great amount of growth on the hand pollinated squash.

Good luck!