Why don’t poison frogs poison themselves?

As the young scientist explained, the mutation involved a single aminoacid in a protein key for survival. Such "simple" mutations can happen in a relatively short span of time. Natural selection makes it possible for the frogs with ability to make such change to survive. Survival of the fittest. Yes, maybe a few generation died and the ones that remained were the ones with the survival trait...

The toxins originate in the insects that the frogs eat. Presumably, when the first frogs ate these bugs, most of them DID die, but those that had the mutation did not and thus the mutation spread.

Possession of these mutations allowed certain frog in the population of frogs to eat insects that they could not otherwise eat. That provided a selective advantage to those that could take advantage of this nutrition, while others without the mutation had to be more choosey and spend more time finding food.

Epibatidine is a potent toxin and thus exerts strong levels of natural selection on organisms that are exposed to it. It is no wonder that they evolved resistance. As for why the same mutation evolved in the same place three separate times, there is constraint in how the protein functions that limits the sites at which replacements can appear without severely (i.e. lethally) compromising the protein's function. There is also the idea that convergent phenotypes in closely related animals are likely to have the same genetic basis while convergent phenotypes in distantly related organisms are likely to have a distinct genetic basis, given other evolutionary changes. In the grand scheme of things, these frogs are closely related (less than 20 million years), and thus it is not so surprising that they have the same changes. (Here is the citation for that idea: http://www.eeb.cornell.edu/agrawal/blog/wp-content/uploads/2017/03/Agrawal-2017-Am-Nat-Convergence.pdf)