What should one who has been afflicted by zina (fornication/adultery) do, having repeated the act despite vowing to Allah to abandon the sin, and who is unable to marry and for whom fasting is no deterrent?

You must genuinely repent from fornication and keep it a secret. To address this sin, you should recognize its gravity and the great reward for those who are chaste. Remember that Allah has associated fornication with polytheism and killing a soul, and has promised "athām" (punishment/sin) to its perpetrator, and negated the perfection of faith from the one who commits it. Be mindful of the seriousness of exposing the girl and her family, and that you would not wish that upon your own family. Hasten to marry, for marriage enriches, and whoever marries for the sake of chastity, Allah will assist him. Fast frequently, as it reduces desire, and you must lower your gaze, stay away from provocations, and keep company with the righteous. Always be mindful of Allah's constant watch over you, and remember the worldly dangers of fornication such as diseases and family disintegration. Consuming henna, reducing foods that stimulate desire, exercising, and engaging in a beneficial academic program may be helpful. If your promise to Allah was in the nature of an oath, then an expiation for breaking an oath is required in addition to repentance.