I've gone for a solution that will work in any version of SQL Server. It will also give more information, as in reality, the sales Dept will want to know by how much it dropped and when the previous order was. It runs at exactly the same speed as Chris's solution on my machine. In order to comply with the competition, I've used Joe's original result and commented out my 'improved' version.

SELECT
    CustomersLastTwoDates.customer_ID,
   'dropped purchase amount on',
   lastOrderDate  
/*   CustomersLastTwoDates.customer_ID,
   'dropped purchase amount by',
    previous.order_amt-CustomersLastTwoDates.order_amt,
   'between',
   previous.order_date,
   'and',
   lastOrderDate  */
FROM
   (SELECT
      lastone.customer_ID,
      lastone.order_date AS lastOrderDate,
      lastone.order_amt,
      DATEADD(DAY, -MIN(DATEDIFF(DAY,d.order_Date,lastone.order_date)),
            lastone.order_date)AS penultimateOrderDate
    FROM DailySalesTotals d INNER JOIN
       (SELECT latest.customer_id, latest.order_date, latest.order_amt
        FROM    DailySalesTotals latest
        INNER JOIN
               (SELECT  customer_ID,
                       [order_date] = MAX(Order_Date)
               FROM    DailySalesTotals
               GROUP BY customer_ID) lastPurchase
       ON latest.customer_ID= lastPurchase.customer_ID
       AND latest.order_Date=lastPurchase.order_date) lastone
   ON   lastone.customer_ID= d.customer_ID
   AND lastone.order_Date> d.order_date
   GROUP BY lastone.customer_ID, lastone.order_date,lastone.order_amt
   HAVING MIN(lastone.order_amt-d.order_amt)<0
   ) CustomersLastTwoDates
INNER JOIN DailySalesTotals previous
ON previous.customer_ID =CustomersLastTwoDates.customer_ID
AND previous.order_Date=CustomersLastTwoDates.penultimateOrderDate
WHERE CustomersLastTwoDates.order_amt < previous. order_amt

Ed: entry copied from Simple-Talk's version of the competition

SELECT  customer_id, 
        ' dropped purchase amount on ',
        MAX(order_date)
FROM
(
SELECT  ROW_NUMBER() OVER(PARTITION BY customer_id ORDER BY order_date DESC) AS RowNumber,
        customer_id,
        order_date,
        order_amt
FROM DailySalesTotals
) AS st
PIVOT
(SUM(order_amt)
FOR RowNumber IN ([1],[2])
) AS PivotTable
GROUP BY customer_id
HAVING MAX([1]) < MAX([2])
ORDER BY customer_id