I don't think it's really a matter of willpower. I experienced multiple burnouts because depression was not an option: I was the black sheep of a demanding and successful family which demanded that I play that role for them, but also demanded that I accept I was really a genius capable of anything, and therefore morally at fault for not achieving everything. I was the chosen one… who'd gone terribly wrong.
As such, I was twisted enough that years of therapy was in order, but really could not let go. To me, five minutes not fretting about how I was going to think up brilliant things and conquer the world, was five unacceptable minutes of being horribly lazy. That's not willpower, that's serious mental illness.
Burnout is just more evidence that serious mental illness is NOT good for you or your productivity. More pressure, past some indefinable point, does not make you more productive.
Any healthy person will rebel, balk, drag their feet and call it whatever (no skin off my nose if you call it burnout). A sufficiently mentally ill person will not be able to rebel, or balk, and will HATE themselves passionately for any moment of feet-dragging, and so they will push harder even while they are miserable… but pay a heavier cost.
Think of it as mental rhabdo (for crossfit fans). Because you are so unhealthy you don't respect any of your own limits, you drive your mental muscles into severe organic collapse and end up flooded with poison, and substantially weaker than you were, for a considerable time. It's not failure of will or collapse of attitude, you manage to mentally break yourself until you don't work and can't think or function.
Bad news. Willpower won't get you there because willpower doesn't automatically mean self-destruction. 'burning out' in smaller ways is MUCH healthier and better in every respect.