If the phenomena was purely psychological, then it might be possible to overcome it. Possibly, rotating the specific task you are working on, or changing locations, or taking shorter but very intensive breaks (like playing street hocky for 30 minutes), might be enough to prevent the brain from switching into despondency mode and allow a few more hours of high productivity. But if the limit is physical, then switching locations or activities won't help much, the brain simply needs to rest (although perhaps a cooling helmet would work - http://www.news-gazette.com/news/health/health-care/2011-03-... - I can't wait for magazine articles with trendy startup engineers at their standing desks all wearing brain cooling headgear).
I think recent science is discovering that even physical problems with the brain can be overcome. Depression is a chemical imbalance in the brain, but talk therapy has been shown to be effective for it. The act of thinking certain thoughts changes the brain's chemistry in ways that can be either positive or negative.
Say that we find that ego depletion comes from a shortage of blood glucose in the brain. If that's the case, the cure could be as simple as stocking the microkitchens with M&Ms (man, maybe Craig Silverstein had the right idea 14 years ago). It's also known that certain stimulants like caffeine and amphetamines help you overcome your normal mental fatigue limits - the problem is that they often tend to create dependency and lose their effect if you chronically overuse them. The reason for looking into the physical mechanism is that we might then be able to find simple solutions that work and don't have long-term side-effects.
