What is the ruling of Islamic law concerning how to deal with a Muslim man who was religiously committed but then suffered from forgetfulness due to old age, so he repeats his prayers and denies the obligation of Zakat upon him despite possessing wealth?

Zakat (definition) on money must be paid on behalf of your deceased father. Zakat is obligatory for minors and the insane, so your father's frequent forgetfulness does not waive the obligation of Zakat. Zakat can be paid on all possessions owned by the father when the hawl (one lunar year) is due, including the last month's salary. Delaying the payment of Zakat for each month separately when the hawl is due will lead to hardship; therefore, it is permissible to pay Zakat on the total sum of his money when the hawl is due.