Maintaining sustained productivity and enthusiasm
I think you have some imaginary researcher in mind. They may seem to be working but without any productivity. They may take "breaks" by moving from task to task, say working on a problem, getting stuck, working on a lecture, thinking about family, back to the research problem, etc. 

I think there is research that suggests that breaks aid productivity. I've found that active breaks, are very useful when creativity lags. Bike ride. Then back to work. Aerobic things are especially good. 

Taking regular breaks or "breaks when needed" can actually help you avoid burn out. 

But, more important, when your mind gets into a pattern of ineffective thought, hammering at the same problem over and over is less likely to be effective than putting it down for a bit. Even a nap can sometimes break a log-jam. 

My advice is to not try to work past your natural limits. When you feel the need for a break, take one, even if it is only to walk around the room for a few minutes. Even stretching exercises. Anything to get your mind out of the rut that suggested the break was needed. 

Don't over glamorize work. Probably you are misinterpreting what you are seeing in others. 

On the other hand, many people can (occasionally) get into a groove and are very productive for several hours running. There is a flow and you just ride the wave. I used to do that when programming. But you can't schedule it. Serendipity. It comes. It goes.