That is an absolute limit of science, one forced on us by our physical limitations. There are lots of other unanswerable questions. Then there is a whole class of what I call inevitability questions. None of these inevitability questions are answerable. You can't determine the probability of the universe or of life on earth when you have only one universe and one history of life to contemplate.
Statistics require more than one data point.
So, again, it is true that answers always raise new questions. But that does not mean that science will never end. It only means that science can never answer all possible questions, it can never quench our curiosity, it can never be complete. Unanswerable questions, by the way, are what give rise to superstring theory, Gaia, psychoanalysis and other example of ironic science, as well as all of philosophy. As I said in my book, the discovery of extraterrestrial life would represent one of the most thrilling findings in the history of science.