The psychological part of this is something I've been interested in for a while. I don't have a great answer to the question, but I've put together a few parts of the puzzle.
- The psychology of 'self-regulation' (more or less, 'willpower') has found that willpower works like a muscle, so can be trained and improved. To some extent, this spills into concentration too.
Nutrition is also an important factor. The psychologists who research self-regulation use glucose-rich foods to give people's brains a little short-term spike in this ability, but for sustained (real-world) supply of the energy the brain consumes in 'willpower', slow release energy is key, think low GI foods.
- The psychology of immersive focus says that people can manage about 4 hours a day of 'deep work', in two chunks of two hours (or more smaller chunks. I think, going from memory). The 2 hour thing is consistent with my and others' experience of playing in the zone (anecdotally).
These things suggest that 4 hours a day of zone (with a break) seems to be an upper limit. So improving your non-zone level of play is the key to improving your stamina. Someone else suggested practice tired. I think having good reliable fundamentals is part of the answer too.
Something that's bugged me for a long time:
When I was an office-based employee, I had a spell of bad afternoon slumps. (It might have been that I was working very hard and burning myself out. Maybe the 4 hours of deep work, all used up in the morning?)
But when I had a meeting in the middle of the day (in which I was actively participating, not coasting), I would do much better in the afternoon, like I'd hit a reset switch.
I didn't get this kind of effect chatting to people in the office, or resting during lunch, or going to the gym, taking a walk, or power naps (I tried lots of different things).
So I've never figured out quite why that worked for me, but if you could bottle that effect, you'd be onto something really good.