How soon was this after you planted the potatoes? What was the overall temp? Was it in the hottest/driest part of the summer? I can see where potato vines would die prematurely if it was too hot or dry for their liking. Any signs of disease? Look up potato diseases and see if you can find some pictures to try to id what yours looked like when they started dying. Have you grown potatoes before, so that you're familiar with their life cycle? They start setting tubers when they blossom. Then the vines naturally die a month or two later.