The Economist has an amusing reductio ad absurdum in its regular Daily Charts section. At current fertility rates, The Economist predicts it will take 25 generations for Hong Kong’s population to drop from its current 3.25 million to just one - which by their calculations will occur in the year 2798. China and Japan will be down to their last woman around 3500 AD, with Canada holding out until almost 4500 AD.
If you browse through any official projections of population in developed countries, they tend to suggest that the current below replacement levels of fertility are here to stay. But would anyone argue that fertility rate in developed countries will not, at some point, increase?