S.D. Codified Laws § 15-19-31

Whenever any sale has commenced at the time and place specified in the notice therefor and because of the amount of property to be sold or other events beyond the control of the officer conducting it, the sale cannot be completed on that day, it may be adjourned to any of the hours within which such sales may be made on the next succeeding business day by announcement of the officer at the time such adjournment is made.