Assuming your potatoes are getting adequate but not excessive water, it is most likely that either Verticillium wilt or black knot root rot (Colletotrichum coccodes), or both, are causing early dying. The fungi that cause both diseases are soil inhabitants, and you must change the location for growing potatoes to one free of these fungi. Varieties differ in their resistance to these diseases.
Contact your local Extension office more information on potato diseases and resistant variety recommendations.
