This is frustrating! I did the same rocky steep fire trail 5 days this week. Out of the 5 days, I got 2 punctures!!
My current tires are Kenda Kwick 700x30c. However, I just purchased some Kenda Happy Medium 700x40c. Hopefully this helps!
But before I hit the trails again next week. What else can I do/buy to prevent punctures?