For me, perseverance becomes futile when I have more important things to do with the time I am spending on it. For example, the result is not worth the time spent, and I have something else to do which I believe to be more important.
This is not just based on personal preference but also based on societal standards. (Especially when it comes to work related issues.) There are many times I persevere because I believe I need to, not because I want too. Thus, importance of the project is more important that personal preference.
When that happens it is basicly a conscious choice.
If I have nothing better to do anyway, I may persevere out of sheer boredom. But this does not happen much at all. There's almost always other stuff in my head I can focus on.
I'd love to go way deeper in the subject, but I think this is about all there is to it to me.