It has been posted recently on several blogs, that the golden chain of Chabad and the Rebbeyim has been broken, due to the descendants leaving the fold, at least partially. Of course, like any other Rabbinic family from that far back much can be and has been lost. However, I aim to prove that lack of children is a major factor as well. We'll do this sowly, and from the last generation up.
כ"ק אדמו"ר והרבנית זי"ע - CHILDLESS
כ"ק אדמו"ר הריי"צ נ"ע - ONE GRANDCHILD, NO GREAT GRANDCHILDREN
הרה"ח ר מנחם מענדל בן אדמו"ר מהר"ש נ"ע - CHILDLESS
הרה"ח ר' בן-ציון בן הרה"ק ר' אברהם מקישינעוו חותן הריי"צ נ"ע -CHILDLESS
and besides, who am I to defend the "Tsarske Familie"?