This past growing season (2011) I was growing squash. Often I would find that the leaves had drooped (lost rigidity). Watering the plant seemed to help; but I'm not sure if there is a causal link there. The season was a particularly dry and hot season. What is the cause of this droop?
Mulch the soil around the plant. This greatly reduces moisture loss, and (with some materials) also reduces weeds. Opinions vary on best materials. See this post. For myself, I don't use -cides on my lawn, and I bag the clippings and use some of them on the garden. You need to make sure to not put too much on at one time, especially when damp, because it can burn from too much nitrogen - just like leaving piles of clippings on the lawn can make yellow spots. Of course, this brings some weed seeds in with it, but it's not a big problem.
If your soil drains quickly, you should increase the humus content, one way or another. Composted cow-manure, dried and bagged from your local home-improvement box store or garden center, is an easy, high-quality fix. I use both that (in the spring, as needed) and winter rye, a tall annual grass that I broadcast in the fall, and then fork into the soil a few weeks before pea-planting. I've had problems with compost from my own bins, and now only apply it in the fall to the vegetable garden, forking it in. The compost usually has woody material left in it that, if left on the surface, harbors earwigs and other critters that sometimes eat the leaves off young plants.
Mulch and humus should get you to where, even on days in the nineties, you don't need to water more often than once every day or two.
When you water, water thoroughly, then try to not water till the top quarter-to-half-inch is dry. This will encourage deeper root growth, making plants more tolerant of hot days. When a hot day is predicted, be sure to water if you think it will wilt before you can water it again, regardless.
For squash in particular, beware of the squash vine borer. If your plants wilt and then outright fail, it's a likely cause. If you ever see something that looks like a handsome bright red and black wasp around the squash, usually in May or June, that's the bugger. It lays eggs on the stem at bottom of the young plant, which bore in and live inside the stem, growing into a big fat ugly grub. The most obvious telltale is some sawdust-like "frass" that it leaves around the base. You can also often see the holes, especially late in the season. Check out the pictures on the Wikipedia link. We've struggled with these guys for many years. Last year we had good results with a resistant variety of squash.
What you are describing sounds like wilting, and it can happen to any plant, not just squash. Watering the plant helps (it is a causal link) because you are restoring water the plant needs to maintain tissue rigidity.
The best treatment is prevention. If the plant gets to a point where it wilts that means it has been damaged. Watering will help restore it, but it will not perform as well as if you had kept it properly watered. In hot, dry weather make sure the plant gets enough water, and do what you can to conserve soil moisture.
"Gardening When It Counts: Growing Food in Hard Times" by Steve Solomon has a lot of material devoted to watering. Among numerous other things, he suggests growing fewer plants to avoid soil moisture loss due to transpiration from a larger number of plants. Thus you can water less and maintain the same soil moisture level, and your per-plant yield will be higher than if you had more plants. (I recommend this book; it has a much more detailed discussion than I can provide in an answer on this site.)