Praise be to Allaah.
It is not permissible for your father to neglect prayer, because neglecting prayer is kufr (disbelief). See the answer to Question # 2182 and 10094.
Your father must beware of the consequences of this action, which is that he is telling others to do what is right but not doing it himself, and forbidding them to do what is wrong but doing it himself. There are severe warnings to those who do this.
It was narrated that Usaamah ibn Zayd said: “I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say, ‘A man will be brought on the Day of Resurrection and will be thrown into Hell, where his intestines will be spilled out and he will go around like a donkey goes around a millstone. The people of Hell will gather around him and say: O so-and-so! What is wrong with you? Didn't you use to order us to do good deeds and forbid us to do bad deeds? He will reply: Yes, I used to order you to do good deeds, but I did not do them myself, and I used to forbid you to do bad deeds, yet I used to do them myself.’”
(Narrated by al-Bukhaari, 3027; Muslim, 5305)
Your duty towards your father is to try your best to call him (da’wah) and tell him that it is obligatory to do the prayers, with wisdom and beautiful preaching. Your eagerness to guide your father is one of the greatest ways in which you can honour him. You have to be patient when doing that, and strive hard in making du’aa’ that he will be guided.
Remember the story of Ibraaheem (peace be upon him) and his father, who was calling him to shirk, and how Ibraaheem replied to him and was kind and gentle in the way that he spoke to him.
And remember the story of Abu Hurayrah with his mother, and how keen he was to call his mother and guide her to Islam. Perhaps (these stories) may encourage you to strive in calling your father.
It was narrated that Abu Hurayrah said: “I used to call my mother (to Islam) when she was still a mushrikah. I called her one day and she said something about the Messenger of Allaah (peace and blessings of Allaah be upon him) that upset me. I went to the Messenger of Allaah (peace and blessings of Allaaah be upon him), weeping. I said, ‘O Messenger of Allaah, I was calling my mother to Islam and she refused. I called her today and she said something about you that I upset me. Pray to Allaah to guide the mother of Abu Hurayrah.’ So the Messenger of Allaah (peace and blessings of Allaaah be upon him) said, ‘O Allaah, guide the mother of Abu Hurayrah.’ I left, feeling hopeful because of the du’aa’ of the Messenger of Allaah (peace and blessings of Allaah be upon him). When I got home, I went to the door and found it slightly ajar. My mother heard my footsteps and said, ‘Stay where you are, O Abu Hurayrah!’ I could hear the sound of water. She bathed and put on her garment, and hastened to put on her khimaar, then she opened the door and said, ‘O Abu Hurayrah, I bear witness that there is no god but Allaah and I bear witness that Muhammad is the Messenger of Allaah.’ I went back to the Messenger of Allaah (peace and blessings of Allaah be upon him) weeping with joy. I said, ‘O Messenger of Allaah, Allaah has answered your prayer and guided the mother of Abu Hurayrah. He praised and thanked Allaah, and said good words. I said, ‘O Messenger of Allaah, pray to Allaah to make me and my mother beloved to the believers and make them beloved to us.’ The Messenger of Allaah (peace and blessings of Allaaah be upon him) said, ‘O Allaah, make this little slave of Yours – meaning Abu Hurayrah – and his mother beloved to Your believing slaves and make the believers beloved to them.’ No believer heard of me or saw me but he loved me.”
(Narrated by Muslim, Fadaa’il al-Sahaabah, 4546)
May Allaah help us all to do that which He loved and which pleases Him.