This can be caused by two things. One is fluctuating moisture levels within the soil, and the other is root knot nematodes. If nematodes are suspected, check the part of the root closest to the plant for small necrotic lesions in the sweet potato. If nematodes are found, use a resistant variety in future plantings.
Contact your local Extension office to inquire about their diagnostic services. They should be able to determine the presence or absence of nematodes.