Praise be to Allah.Praise be to Allaah.
If the matter is as you describe, then your grandfather is not obliged to pray, because of his losing his mind, The Prophet (peace and blessings of Allaah be upon him) said: “The Pen has been lifted from three: from the sleeping person until he wakes up, from the minor until he grows up, and from the insane person until he comes to his senses.” Narrated by Abu Dawood (4403), al-Tirmidhi (1423), al-Nasaa’i (3432) and Ibn Maajah (2041). Abu Dawood said: It was narrated by Ibn Jurayj from al-Qaasim ibn Yazeed from ‘Ali (may Allaah be pleased with him) from the Prophet (peace and blessings of Allaah be upon him), and he added: “And the one who is senile.” This hadeeth was classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Senility refers to when a person loses his mind as the result of reaching a great age. It is stated in ‘Awn al-Ma’bood that the report which mentions senility is da’eef (weak) because of the isnaad, but something which suggests that the meaning is valid was narrated from al-Subki. Al-Subki said: Senility may be added to these three, and it is valid. What is meant thereby is an elderly man who has lost his mind due to his great age. An old man may become confused and unable to distinguish things, which may mean that he is no longer accountable, but he is not described as insane, because an insane person may be treated whereas a senile person cannot be treated. Hence it does not say in the hadeeth “until he recovers”, because in most cases he cannot recover from it, until he dies. If he does recover from it sometimes and comes back to his senses, then he is accountable again. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) explained that senility means that one is no longer accountable: Fasting is not obligatory unless certain conditions are met: one, being of sound mind; two, being an adult; three, being Muslim; four, being able to do it; five, not being a traveller; six, being free of menses and postpartum bleeding (nifaas) in the case of women.
1 – Being of sound mind, the opposite of which is having lost one’s mind, whether that is due to insanity or senility, i.e., old age, or because of an accident which has caused one to lose one’s mind and sense of awareness. Such a person is not obliged to do anything because he has lost his mind. Based on this, the old man who has reached the stage of senility is not obliged to fast or feed poor persons instead, because he lost all sense of reason. Similarly the one who loses consciousness due to an accident etc is not obliged to fast or feed poor persons instead, because he is not of sound mind. End quote from Liqa’ al-Baab il-Maftooh.
To conclude, the person who has reached the stage of senility and has no sense of time and cannot distinguish between the prayers is not obliged to pray.
If your mother has taken care of what your grandfather needs, such as food and drink, etc, and she thinks it most likely that his calling for her is not due to some need, and it is just because of his senility, then there is no sin on her if she does not answer him, especially since that is causing her hardship.
And Allaah knows best.