Further research showed that older rejections (some more than 6 months old) were in the system, and even though charges were paid subsequent to that rejection, the next rejection forced the Payment Method to CK.  This is because rejections are cumulative, regardless of time.

The following query will display all the Transaction records that fall into this category (where they were rejected beyond 30 days in the past):

SELECT T0.* FROM   TRANSACTIONS T0
WHERE  T0.ACCOUNT_ID IN (SELECT ACCOUNT_ID
                    FROM   ACCOUNTS
                    WHERE  STS = 'A')
AND    T0.TRANSACTION_TYPE = 'PL'
AND    T0.GIFT_KIND = 'SG'
AND    T0.PAYMENT_METHOD = 'CK'
AND    T0.BANK_REJECTION_COUNT = 2  -- Remember to use your system's CP rejection count here
AND    EXISTS (SELECT 'X'
       FROM   TRANSACTIONS T1
       WHERE  T1.ACCOUNT_ID = T0.ACCOUNT_ID
       AND    T1.PLEDGE_NUMBER = T0.PLEDGE_NUMBER
       AND    T1.BANK_REJECTION_COUNT = 1
       AND    T1.PROCESSED_DATE < T0.PROCESSED_DATE - 30)
ORDER  BY T0.GIFT_DATE DESC, T0.ACCOUNT_ID, T0.GIFT_SEQ DESC, T0.ADJUSTMENT_SEQ DESC;