YR,
I don’t know how long a generation lasts for. But I do know that people just a few years older than me remember and saw the Rebbe. Does a generation finish when the Rebbe is Nistalek? It obviously doesn’t go on forever, but being that there is no new Rebbe, it definitely continues for some time. I know what you will ask now, “Why didn’t the Rebbe appoint someone in his stead? Why didn’t Chabad appoint a new Rebbe?”
I can’t answer for the Rebbe, but I can tell you that the Rebbe had no children, and there was definitely no obvious worthy candidate, we have no one close to the Rebbes stature. The Rebbe did leave detailed instructions for after his passing, and instructed that Chassidim listen to Chassidishe Rabbonim and Vaadei Rabbonei Chabad be established in every community, among other Horaa’ors.