If anyone is a believer in solving challenges through sheer force of will, it's me. I'm a stubborn man and I am the son of an even more stubborn man. I don't believe in the word "quit" and I don't believe in giving up. I am however - as are you, finite. We all have limited resources. We get tired: physically, emotionally, spiritually. I have observed that there are moments we arrive at in problem solving where we have so depleted our personal resources that continuing to stare at a computer screen and carry on becomes counterproductive.
Sometimes the best thing you can do is to walk away from a problem and get some rest.
More times than I can count, I have revisited a problem with fresh eyes and a clear head and suddenly a challenge that seemed perplexing had an amusingly simple solution.
Know your limits and respect the healing value of rest.