Assuming that the column EnRID is a unique row id, try this:

UPDATE Enrollment SET ISMID = NULL

 WHERE Enrid IN (SELECT MIN(E.ENRID)

                     FROM ENROLLMENT E INNER JOIN

                                     (SELECT ismid, Mydate

                                        FROM enrollment

                                       WHERE ismid IS NOT NULL AND active = 1

                                       GROUP BY ismid, Mydate

                                      HAVING COUNT(*) > 1) x ON E.IsMid = X.IsMid AND E.MyDate = X.MyDate

                              GROUP BY E.IsMid, E.MyDate

                             )

   AND ACTIVE = 1

Have a great day

Wayne