Is seeking forgiveness for a sin that is still being committed considered mockery of the Lord or an act of disbelief (kufr), and does it invalidate the fasting of the first day of the expiation for an oath?

There is no necessary connection between disbelief and repeated sin; persistence in major sins does not expel a servant from the fold of Islam. As for the benefit of seeking forgiveness (istighfar) while not abandoning the sin, scholars have differed on this. Some believe that seeking forgiveness verbally while the heart insists on the sin is merely a supplication that benefits its owner if Allah answers his prayer, but persistence might prevent its answer. Others emphasize the condition of repentance for the acceptance of seeking forgiveness, and they view seeking forgiveness verbally while being engaged in sin as a form of trifling. What appears to be the case is that verbal seeking of forgiveness benefits its owner if it is accompanied by a dislike of the sin, a desire to abandon it, and sincerity of heart in turning to Allah, unlike someone whose tongue seeks forgiveness but whose heart is heedless or attached to the sin.