Is the failure to fulfill a vow to memorize the Holy Quran the reason for her and her son's recurring illness?

Memorizing the Quran is among the best acts of obedience. Fulfilling a vow is obligatory for one who has vowed an act of obedience to Allah, and it is not permissible to break it except in case of inability, in which case an expiation for breaking an oath becomes due. It is permissible to delay fulfilling a vow for one who is unable to fulfill it immediately, unless the wording of the vow specified a certain period for its fulfillment. There is no necessary connection between not fulfilling a vow and illness; for illness and affliction are from Allah's decree and destiny, and sins are among their causes. A Muslim must be patient, supplicate for well-being, give much charity, and maintain ties of kinship. Ali ibn Abi Talib, may Allah be pleased with him, said: "And whatever strikes you of disaster – it is for what your hands have earned; and He pardons much." And the Prophet, peace be upon him, said: "No calamity, be it greater or lesser, befalls a servant except due to a sin, and what Allah pardons is far greater."