What is entailed for one who vowed to pray two Rak'ahs if he committed a bad habit, then became unable to uphold the vow?

A vow taken as a means to deter from doing something or to push towards doing it is called a "vow of obstinacy" (nadhr lajaj). Its maker has the choice between fulfilling it or offering an expiation (kaffara) similar to that for a broken oath (kaffarat yameen). The expiation does not multiply with the repetition of the action unless the wording of the vow necessitates repetition. If the expiation was repeated and you do not know the exact number of times, then what is obligatory upon you is the lowest certain number, because the default is the acquittal of one's liability. However, what is more precautionary is to expiate for the doubtful amount.