you probably have a case of powdery midew

Symptoms:
Powdery mildew is a fungal disease that affects most cucurbits, and in fact, many other species as well. Infection is first noted as slightly chlorotic spots on leaves. A white powdery appearing "dust" quickly covers the leaf surface, and affected leaves gradually turn brown and papery.

Control:
Use of resistant varieties and/or preventative fungicide sprays are both important. Since the fungus also infects many weed species, good weed control in and around production fields is important. Disease development is favored by cool, dry weather.

I don't think it's a Mildew problem.

His problem is the oil. Once a week seems just way too much to me. I also read before that you need to be very cautious with it because it does cause your leaves to dry out and burn.

It looks to me that's exactly what's happening. I would be surprised if the directions in your oil application didn't already warn you about this.

I killed like 3 leaves on my pumpkin vine early in the year because I didn't read the label. You aren't supposed to use some oil pesticides together with sulfur fungicides, they react or something and damage the plant. But it wasn't as bad as the label made it sound.

I'll check the bottle again, but I thought it said once per week maximum. I don't know what's better, let the aphids take over and eat the plant up, or over spray the neem oil! I don't know how to get rid of those stupid aphids...every freaking year it happens. Last year I tried neem oil one week, then dish soap the next week and alternated. Didn't matter, they still destroyed the place.

Wouldn't powdery mildew make the leaves shrivel up and die? These don't really die, just start changing colors and eventually (at least a month later) die to a burnt brown.

Yea it takes them a while. They can be completely infested with the mildew and still be feeding water and nutrients to the leaf. It's a very successful parasite, I can tell you that much.

Go down to your garden center, and either buy a bag of ladybugs or preying mantids. As long as you have those aphids running around, the police won't bother moving to another garden.