If a customer has signed up for automatic payments for safe deposit box rent (on an annual basis), do we need to send a notice to the customer informing them that the payment will be made on X date?

There's no requirement that you do so, unless you agreed to in the contract or authorization form for the automatic payments. I know that my bank does not send a notice of the impending payment. However, given the fact that there's a full year between those payments, a notice might be helpful to customers, especially those who might keep low balances.