What is the ruling on not fulfilling a vow made to Allah to perform specific acts of worship upon committing a particular sin, especially when feeling remorseful and finding it difficult to perform these acts of worship on the same day?

A Muslim must avoid sins. If you promised Allah to abandon a certain sin, and your intention was merely a promise and not a vow (nadhr), then there is no expiation required of you if you fall into that sin; rather, you must repent and not return to it. However, if your intention was a vow, then it is a "vow of contention" (nadhr lajaj), and its maker has the choice between fulfilling the vow or offering an expiation for breaking an oath (kaffarat yamin). The expiation is repeated every time the sin is committed if the صيغة (wording) was "every time I commit such-and-such a sin."