Rolling Delinquency - Can we refuse a payment?

We apply a payment on a delinquent mortgage to the oldest outstanding payment due - which then advances the date that the borrower's delinquency began.
If the borrower is past due for the 9/1/17 payment, and they make a regular payment on 10/5/17 - the payment satisfies the 9/1/17 payment, and the borrower is now past due for 10/1/17. The borrower will always be 30 or more days past due.

Question: Is the Bank able to NOT ACCEPT the 10/1/17 payment if the 9/1/17 payment is not paid at the same time?

Have you read this?

https://s3.amazonaws.com/files.consumerf...Delinquency.pdf

Look at the last section on page 3 and top of page 4. I would suggest discussing with counsel regarding your note and any other limitations.

Thank you very much!!