Randy, here's what I experience with peppers. I grow them in cages to help support the fruit crop, add a lot of compost below the root ball when I plant, and insert a plastic watering tube about 18 inches into the soil next to the plant. I water heavily once a week - otherwise I get wilt, especially if there's a heavy fruit crop and the plants are large with lots of foliage. My plants alway get thick woody main stems. I've never had any die on me though as you described. I'm wondering if you're doing a lot of surface watering, thus the roots don't penetrate deeply into the soil and the plant eventually over grows the roots? Just some of my thoughts and I don't know for sure what your problem may be.