I have looked to state law, and not found anything specific in regards to if a single party held safe deposit box owner is deceased, but also maintains an account that automatically makes payment for the box, how long does the bank continue to make the payment? If the account is restricted by the bank due to death of the owner, can it still make the payment for safe deposit box rent. Or does the payment cease at death and the box contents would be considered abandoned or unclaimed?

You need to cease debiting the account, if you have actual notice of the death the customer (and do not say you saw it in the obits). At the time someone presented the death certificate or other paperwork, the box should have been called to their attention. Otherwise, if money is owed on the box, you treat it like any other past due box.