Many environmentally-minded people have the impression that fixed natural resources, in principle, makes perpetual economic growth impossible. This seems to make sense from an input-output perspective: growing output requires growing input (true); however some of the required inputs are fixed (true); hence output must stop growing eventually.
However the mistake is this: growing output requires at least one growing input. If the growing input can substitute for the non-growing inputs, then it is mathematically possible for the limiting point (zero natural resources) to be reached at time infinity - with economic growth happening all along the way.
What can be this perpetually growing input? In human history, economic growth has typically been driven by technology. Technology ultimately is based on human intelligence, or information processing.
It seems that the ability to discover new stuff is limitless. That is, it seems that humans will also be able to discover new things that the market values. This is the crucial point: economic growth is not just a matter of piling up new stuff by weight. Then certainly economic growth is limited. Economic growth is a matter of piling up new stuff by market value, based on subjective assessment of individuals, collectively summed up in the market price. This process holds the key to perpetual economic growth.
Scattalaxis has another way of putting it. In addition to the economic sphere and the biosphere is the "noosphere" (was this originated by de Chardin?) The products of the noosphere appear to be limitless, as valued by the noosphere itself.
Now all of these are possibilities are based on theory. On the other hand perhaps humans will run out of innovations, or perhaps inventions are not as substitutable with natural resources as we think. For example, perhaps it is not possible to find a cheap substitute for oil-powered transportation.
In the long run, my money is on the human mind.