“Note the Rambam never discusses what happens if the bchezkas moshiach passes away naturally. He only says two things disqualify: If he is unsuccessful or if he is killed”
In the interest of intellectual honesty, I’d like to point out the before Gimmel Tammuz, it was very Poshut to any Lubavitcher that Moshiach must come from the living. No one had ever come up with these diyukim of “it says Nehrag, not meis”. After Gimmel Tammuz however, many now realized that they had a problem reconciling their beliefs with the unfortunate reality. So there were two approaches, one was “true, Moshiach must be alive, but the Rebbe simply never was Nistalek, he’s still alive in a Guf Gashmi”, the other approach is that of course, the Rebbe passed away, however, Moshiach could be Min HaMeisim. While the second one is obviously less delusional, nobody would have ever thought that way before Gimmel Tammuz.