Is it permissible, in Islamic law, to discontinue psychiatric medications that improve a patient's condition, based on the advice of a reciter [of Qur'an] who believes that treatment with the Qur'an alone is sufficient to cure the schizophrenia that has afflicted her for more than twenty years?

Ruqyah Shar'iyyah (Islamic exorcision/healing) is beneficial for all ailments, but healing is by the decree of Allah. There is no contradiction between psychotherapy and Ruqyah Shar'iyyah, so one should combine both, especially if the illness has been diagnosed. The proof for not abandoning medicine is the Prophet's (peace and blessings be upon him) urging to seek treatment. If the illness is known, the principle is to take medicine along with Ruqyah. However, if it is unknown, it is preferable to reduce medication and focus on Ruqyah. Sheikh Abdullah Al-Mutlaq emphasizes that treatment is Islamically mandated, and that Ruqyah and medicine can be a means for healing together, and that it is not permissible for the one performing Ruqyah to ask the patient to abandon medical treatment. In summary: If your sister's illness is known, do not stop the medicine, and combine it with Ruqyah Shar'iyyah.