How can I help my grandfather, who is suffering from a mental illness that sometimes causes him to lose consciousness, to recite the Shahada while he is on his deathbed?

It is good to strive for your grandfather's conversion to Islam. The Prophet, peace and blessings be upon him, tried with Abu Talib, and if he utters the word of monotheism before death, that will benefit him. If he is conscious, remind him gently. If he pronounces the two testimonies of faith, he enters Islam. If he is unable to speak but can read, write the two testimonies for him and explain them. If he has been suffering from a mental disorder from the beginning, then he is not accountable.