There seem to be two problems with that model. The first is that the probability only approaches zero as N approaches infinitity (i.e., an infinite number of generations; although of course it can get quite small depending upon the value of k). The second is the assumption that the model provided actually fits the probability of survival, which it doesn't in the case of more than one offspring carrying the mitochondrial line (unless you're taking this into account with the k that "may vary from step to step", in which case the expression doesn't really have a discrete meaning).
For example, take the potential real-world model of a tribe where women traditionally have two female children, and whose chance of those children dying (their "k" in your model) before they have two female children is 25%. The probability of survival of the mitochondrial line in one generation is two 75% chances, or about 93%. However, the probability of survival in the next generation, assuming that 1 of the four offspring died (that 25% factor) is 98%, and we now have a function with a growing population and with a probability of survival that is approaching (but never quite reaching, of course) 1, rather than zero.
I understand how you came to your conclusion now, however.