I realize many math problems solved by mathematicians require a tremendous perseverance over a period of years. My question is not about endurance over a long period of time, but over several hours.
I can only spend an hour and a half to two hours working through problems or reading textbooks until my mind becomes cloudy and then I need to take a 30 minute to 1 hour break in order for me to make anymore meaningful progress. This was never a problem when I was an undergraduate since exams were at most 2 hours long. But I realize there are qualifying exams and math competitions like the Putnam exam where contestants solve problems in 3 hour chunks.
How does one develop the stamina to concentrate for so long in a single sitting? Should I continue to do math even though my mind is fatigued?
How important is it for a professional mathematician to be able to work on a problem for a long period of time in a single sitting?