Answer:
Concerns for any lapse of payments notwithstanding, the bank has no authority to continue to allow ACH debits from the account if the sole owner of the account is deceased.
I'd take whatever steps you can reasonable take to verify the death of your customer. That done, I suggest you write to the estate of the deceased at the address in your files, indicating that you've been notified of the death and must now terminate activity from the account. Including a list of regular debits would be a service to any family who might read the letter.
Then start returning the debits.
First published on BankersOnline.com 121/06/04