Here is the link that makes me think it is downy mildew. My dead watermelon leaves look just like the ones here:
http://www.maine.gov/agriculture/pesticides/gotpests/diseases/downy-mi ldew.htm

Another downy mildew link:
http://cuke.hort.ncsu.edu/cucurbit/wmelon/wmdshndbk/dm.html

What I don't understand is that everything seems to have it, even the weeds. The drought we are having makes the weeds die off from the base upwards. I took a pic of a leaf from some pigweed and it looks just like the leaves from my muskmelon. Fungal disease is supposed to be spread by cool, wet weather. But we are having the opposite.

Does drought cause fungal disease, too? The leaves that wilt from lack of water and heat are what seem to get the mildew.

I sprayed Daconil tonight. I read to spray fungicide every five days. I can rotate copper and sulphur with the Daconil.

Last year in our awful drought my melons got a bad case of powdery mildew, entirely different disease.

Your lack of fruit set could also be related to lack of water. I water mine with about 2 inches every 5-7 days. When they start wilting midday, they need a deep watering. A little every day probably isn't as good.

I think you said they wilt every day. That's probably too dry. After a good deep watering they shouldn't wilt mid day even at 105F.

I water them every day and sometimes let the water run for hours. It gets at least one hour a day minimum. The ground is soft under the plastic and when I pull a weed from it, the soil seems to be nice and moist. The muskmelons wilt from the heat even while the water is on.

The pigweed might have a nitrogen deficiency, but I would think that had something to do with drying out from the heat being the real cause of it, rather than a deficiency in the soil.

http://westernfarmpress.com/powdery-mildew-melons

"P. xanthii prefers dry conditions, with relative humidity of 50 percent to 90 percent for spore production. Although relative humidity doesn�t often reach those levels consistently in the desert, dense foliage and irrigation may create microclimates that favor powdery mildew development. However, presence of water on the plant surface may wash off and/or inhibit the germination of the fungal spores. P. xanthii grows on the outside of leaves, first appearing as a small white growth, eventually becoming a layer of white fluffy mycelium and spores on the upper or lower side of leaves. P. xanthii does not grow systemically (able to spread through the inside of the entire plant), instead this fungus prefers to produce mycelium on the outer surface, and penetrate the leaves with specialized feeding cells called haustoria. The fungus will then produce spores in the absence of free water; spore production gives the leaves the characteristic powdery appearance. The spores are spread to new infection sites by wind. After the fungus has extracted nutrients, the plant cells die, causing the leaves to become brown and papery. Fruit produced by the plant may accumulate less sugar, have reduced yield, and shortened production times."

Not many things like water every day. That can cause the roots to rot which causes loss of leaves. Don't water your melons more than once every 3 days. If you can't extend the interval that long at least you are wetting too small an area around each plant.