When did Martin Luther lose his Apostolic succession according to Catholic and Eastern Orthodox Churchеs? As far as I understand Martin Luther according to the Catholic and the Eastern Orthodox Churches possessed the Apostolic succession while he was in the Roman Catholic Church (he was a priest, after all). However, now both Luther and all his followers are considered by both Catholic and Eastern Orthodox Church as those who don't posses the Apostolic succession. So, according to them, at what particular point Martin Luther lost his Apostolic succession?
According to the Catholic Church, the short answer is that he never lost it. In fact, in the strict sense, Martin Luther never participated in apostolic succession to begin with.

Apostolic succession refers to the fact that all bishops can trace their holy orders all the way back to the Apostles. That is, the Apostles ordained certain men bishops (or what we would call bishops today) by the laying on of hands, and these, in turn, ordained other bishops, and so forth. (See Catechism of the Catholic Church [CCC] 77-79, as well as 1 Timothy 5:22, which is an example in the Scripture of where this kind of succession occurred.) Thus, at least in the strict sense, apostolic succession does not apply to presbyters (i.e., priests).

Since Martin Luther was only a presbyter, not a bishop, he did not (at least in the strict sense) participate an apostolic succession. For example, he never had the capacity to ordain another man bishop. (Only a bishop can confer the Sacrament of Holy Orders. Hence, Luther could not ordain deacons or priests either; see CCC 1576.)

What the O.P. may have been thinking of was the status of Martin Luther’s holy orders.

The Catholic Church teaches that the Sacrament of Holy Orders confers a permanent “mark,” called a character, on the soul of the person who is ordained. (See CCC 1582; it is a “mark” in a metaphorical sense, of course: the character consists in the capacity of the ordained minister to perform the ministry that he is called to, especially the capacity to confer certain sacraments.) This character is permanent, and no power on earth can remove it.

As a consequence, Martin Luther remained a validly ordained priest to the end of his life. His status in the Church became irregular when he was excommunicated in 1521, but that in no way affected his holy orders.

The reason that Lutherans (as opposed to Luther himself) do not maintain Apostolic succession is that they did not attempt to continue it. Luther himself, as I mentioned, was only a presbyter, so he could not ordain new bishops, priests, or deacons.

Doctrinally, Luther largely disavowed the concept of the ministerial priesthood, so he did not seek to continue it. In any event, in order to do so, he would have had to have the cooperation of a Catholic bishop (or at any rate, a validly ordained bishop, such as an Orthodox bishop), which was not likely during his lifetime. Consequently, although many first-generation Lutherans were priests, their holy orders died with them.