Is it obligatory to repay a deceased father's debt to a bank after more than ten years have passed since his death?

If your father's debt to the bank was an interest-based loan, then you are not permitted to repay the bank anything more than the remaining principal. You should not pay the interest unless you are forcibly compelled to do so, while seeking forgiveness for your father. If the debt was a benevolent loan (interest-free), then you should repay all of it from his own money. If he does not have money, it is recommended for you to repay it from your own money if you are able, based on the Prophet's (peace be upon him) saying: "Indeed, the gravest sins with which a servant meets Allah, after the major sins He has forbidden, are that a man dies owing a debt for which he leaves nothing to repay it." If you are unsure about the nature of the debt, then repay all of it, for repaying debts is obligatory.