"Never give up" is bad advice?

Probability of success if you continue: small. Probability of success if you give up: zero.

Small is better than zero, am I right?

On the other hand, this analysis only matters if the cost of failure is no worse than the cost of giving up. The "rational" thing to do would be to give up if and only if (probability of success * utility of success) + (probability of failure * utility of failure) < (utility of giving up).

There are a lot of things that one can achieve through sheer persistence, but there are others that, well, you can't do, period. The trick is to be able to tell the difference. I suspect that I'm not going to be a star athlete no matter how much I practice, but I just might qualify for the Pro Tour some day.