I believe you might have the beginnings of bacterial wilt. Look at my response and the links I gave for "Drooping Leaves" on July 2 2010.

Note in the articles the test where you cut one of the branches and see if the sap is milky and sticky.

That they revive at night and in cool weather suggests that your squashes aren't able to draw enough moisture to compensate for the water they transpire during the warm hours of the day. There are a couple of things I think responsible for this very common problem.
1) Seeds planted from starter pots instead of direct seeded will never be as deeply and well rooted.
2) Squashes want to put out roots as their vines grow along. If your vines lay across moist soil, they will be able to draw up much more water since they will have roots all over the place drawing moisture. If you just water the base of the vine, that leaves the main stem responsible for delivering water to all the distant leaves. Even bush-type squashes can suffer this way.

The people who grow the best squashes grown them over large areas of cultivated soil. The roots are thus able to draw over a large area. Most home gardeners can't do this.

I think #2. These plants were volunteers.
Thanks,