Superstrain of powdery mildew

I have a few spots of powdery mildew on a couple of my plants. First I hit them with a regular strength Neem solution. The mildew was still there. Then I hit them with pure Hydrogen peroxide ( regular strength that you find in stores ). The mildew was still there. Finally, I mixed up a double strength batch of neem and hit them. The mildew is still there.

I haven't had this before, and I have read claims that peroxide kills it instantly...also neem is SUPPOSED to fix this.

What gives ?