Instead of running that in a loop, why not issue just the one command? SQL has an IN clause:
UPDATE submit SET submit_status ='S' WHERE submit_id IN (list)
All you have to do is build the list:
StringBuilder sb = new StringBuilder();
sb.Append("UPDATE submit SET submit_status ='S' WHERE submit_id IN (");
sb.Append(string.Join(",", edit_list));
sb.Append(")");
cmd.CommandText = sb.ToString();