Can we extract too much of a biotic resource from a natural ecosystem?

This is definitely possible. Ideally, all ecosystems exist in a balanced state where each organism plays a role and has its own niche.  If too many of one organism are suddenly removed from an ecosystem, all organisms that are connected to it would suffer.

In in the case of a second level consumer being over hunted, predators consuming that particular animal could suffer starvation because one of their food sources is in short supply.  The animals usually eaten by the second level consumer could also suffer starvation since their numbers would not be controlled by their usual predator.

 Over time, however, the ecosystem would usually return to a balanced state.