[Lucky Dog]

This part isn't quite right. I don't think any species gradually mutates itself into extinction. Rather, due to environmental changes (climate, predators, whatever), it's unable to survive.

Thank you for the clarification. The first part, then, is correctly summarized?

Let me restate: Perhaps, then, it is the failure of a species to accumulate the requisite number of favorable mutations to resist the negative changes in natural selection pressure that leads to extinction.

[PatrickHenry]

Let me restate: Perhaps, then, it is the failure of a species to accumulate the requisite number of favorable mutations to resist the negative changes in natural selection pressure that leads to extinction.

I think you're starting from an incorrect premise. It's simpler than you've stated it. A creature either survives long enough to breed successfully, or it doesn't. If it's well-suited for the environment in which it lives, it's likely to make it. If the pond suddenly dries up, tough luck.

But if the environmental challenge isn't quite so severe, some of that population might be able to survive. They'll pass on their genetic material to the next generation. That's the deal. If the environment changes very gradually, some version of the population might just make it, although each new generation is going to go through the filter of a changing environment.