What is the expiation required from someone who swore not to do a specific thing until death, then violated his oath many times with the same type of action before atoning for the first violation? And does the oath become void after expiation, or does it continue until death?

Excessive swearing is reprehensible in Islamic law. Repeated oaths concerning the same matter necessitate repeated expiation if the wording of the oath implies repetition, or if the one swearing intended the expiation to be repeated with the repetition of the action sworn against. Therefore, you are required to offer expiation for each instance of breaking the oath, and a single expiation will not suffice because you intended its continuity. This oath is not invalidated by breaking it and offering expiation; rather, it remains in effect. If you are uncertain about the time of the intention, investigate. If it was at a time other than when the oath was sworn, it has no effect, and the oath is dissolved by a single expiation. However, if it was at the time of swearing the oath, then the oath remains in effect, and the expiation is repeated with each repetition of the action. If nothing becomes clear to you, then the doubt is disregarded, because the original principle is freedom from liability, and certainty is not removed by doubt.