What is required of one who vowed to recite Surat Al-Baqarah daily, then committed a specific sin, and then repeated the sin multiple times without reciting it? Does he have to fast three days for breaking the vow, or is it sufficient for him to recite it for the number of times he sinned?

A vow made with the intention of abandoning a sin is a vow of obstinacy and anger (Nathr Lajaj wa Ghadab). Its ruling gives one the choice between fulfilling it or offering expiation (kaffarah). By doing either of these, the vow is dissolved. If the wording of the vow implies repetition, such as saying, "Every time I do such and such, I must recite Surah Al-Baqarah," then expiation becomes obligatory with each repetition of the action vowed to be abandoned. If the sin is repeated three times and the vow includes repetition, then you owe three expiations or the recitation of Surah Al-Baqarah three times. The expiation for an oath (kaffarat al-yameen) is feeding ten needy persons, or clothing them, or emancipating a slave, or fasting three days for those who cannot afford the former. If a temporary vow is delayed without a valid excuse, there is no expiation for its delay; rather, one must fulfill it and repent.