All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If one grows old but still enjoys his mental capacity, then he is still ordered to pray and he is not free from the obligation. He may pray in the manner that enables him to perform the obligation whether standing, sitting or lying on his side for the Prophet, sallallaahu ‘alayhi wa sallam, said: "Pray while standing and if you cannot, pray while sitting and if you cannot, then pray while lying on your side." [Al-Bukhari, Abu Daawood, An-Nasaa’i, At-Tirmithi and Ibn Maajah]
Man is not free from the obligation of prayer as long as he enjoys his mental faculties because reason is the condition for religious assignment. If he is competent for religious assignment and he prays alone – like the case with your father – then, what matters is his certainty, not that of others, even if he is mistaken, Allaah Pardons him because he did his best within the limits of his abilities in performing the obligation.
It is better for you to help him perform the obligations as long as you are sure of this matter by taking your father to the Masjid to perform the prayer in congregation if this is not difficult for you because by praying in congregation, he is committed to the Imaam.
This is as long as your father possesses his mental faculties and does not suffer senility. If he suffers senility, then prayer is not obligatory upon him and he is not punished for the faults in his prayer.
Allaah Knows best.