Is it obligatory to continue fulfilling a vow to donate five riyals whenever a specific sin is committed, a vow that was not limited by time, or does this vow lapse after repeatedly committing the sin and donating several times?

You must fear God, abandon disobedience, and offer sincere repentance. A vow to abandon sins is not valid because abandoning them is a religious obligation. It is not permissible to vow to perform an obligatory act, as the basic principle of a vow is that it should be for a recommended act of worship. You must repent to God, seek His forgiveness, and abandon sins. It is more cautious and pious to offer an expiation for an oath.