Unless external factors kick in, like depletion of resources and soils. There's no any law of nature that says homo sapiens must be able to survive. Smaller scale examples are:
1. Easter island -- we, humans, deforested the island, that degraded and depleted human population significantly even before the first european ships discovered the island. From what I've heard, "Rapa Nui" movie is unusually historically correct on the events.
2. St. Matthew Island -- 29 introduced reindeer rapidly overpopulated the island and ate all the available food there, so the whole population died.
> Easter island -- we, humans, deforested the island, that degraded and depleted human population significantly even before the first european ships discovered the island.
More recent research shows that this is probably not true - there's evidence that the population was growing right up until the arrival of Europeans[1].
1. Easter island -- we, humans, deforested the island, that degraded and depleted human population significantly even before the first european ships discovered the island. From what I've heard, "Rapa Nui" movie is unusually historically correct on the events.
2. St. Matthew Island -- 29 introduced reindeer rapidly overpopulated the island and ate all the available food there, so the whole population died.
Same thing can happen on planet Earth.