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?
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When Luther was excommunicated for insubordination on January 3, 1521, he lost the ability to say he was in the chain. You cannot succeed someone who has disowned you.
Note the date to which most people would ascribe the "beginning of the Protestant Reformation" (a bad term since it was really a process that had been going on since the 1300s!) is October 31, 1517, when Luther nailed his 95 Theses to the door at Wittenburg Cathedal—a document outlining his beefs with the Catholic church, as it was acting at the time. The heresies for which Luther was excommunicated are not generally given a specific name (unless if you want to call Lutheranism or even Protestantism a "heresy").
1521 might be the Roman Catholic answer to this question, but the Eastern Orthodox answer is a bit harder to give. The Roman Catholic Church lost its apostolic succession in splitting off from the Orthodox Church (remember, this is the Orthodox perspective).
As late as 1274 and then at 1438, there were still attempts at reunion between the Roman Catholics and the Orthodox. But the reaction of the Orthodox people to the attempted reunion in 1438 made it clear that by that time the schism was a fait accompli.
That being the case, in the Orthodox view Luther was already in a church that had lost its apostolic succession, and his actions did nothing to remedy that.
Interestingly, some of the Reformers did have contact with the Patriarch of Constantinople, and explored the possibility of reconciliation between the two groups. Here's an article that gives a good summary of what took place.