What is the ruling on vowing to fast for a lifetime if its cause is abstaining from marriage, and is it permissible to retract it due to hardship?

One should not undertake a vow that prevents them from something Allah has legislated, like marriage, for the Prophet, peace and blessings be upon him, said: "Whoever turns away from my Sunnah is not of me." What you have done is called a vow of obstinacy and anger (nadhir al-lajaj wal-ghadab), and in such a case, you have the choice between fulfilling it or offering an expiation for an oath (kaffarat yamin). This is the view of the Hanbalis and the choice of Al-Nawawi, while the Shafi'i school holds that only an expiation for an oath is required. This is based on what was narrated by Imran ibn Husayn, who said: I heard the Messenger of Allah, peace and blessings be upon him, say: "There is no vow in anger, and its expiation is the expiation of an oath." Therefore, if you wish not to fulfill this vow, you must offer an expiation for an oath: feeding ten poor persons, or clothing them, or freeing a slave. If you are unable to do that, then fast for three consecutive days. Nothing else is required of you. What you mentioned about your family forcing you to marry, if it was a real, compelling coercion, then you would not be breaking your vow. Allah knows best.