What's better, not doing something because we're tired, or doing something despite the tired? Maybe, it's not that black and white.
Our willingness to persist comes from the outpour of the result we want. Take the same person and put them in two wildly different environments and we might get two different results. If someone has a 10-page paper due the next day, she is more likely to persist in the tired if she is with other people with work to get done, too. But, if she is in the privacy of her room with thousands of easy distractions...she might be less likely to finish her work.
The same goes for persistence. Persistence is not just predicated on our own self-will, but the environment we subject ourselves to.