One thing that I noticed is that I can actually think clearly when I am fatigued, and that what is really going on is that being fatigued exaggerates my bad habits. So I actually practiced doing GMAT questions when I was tired, late at night or something, to uncover my bad habits and learn to get right answers even when I was tired.
Another thing that helps is to remind yourself that the section will last for only another 15 minutes, maybe take a short mental break for a minute, and dive back in. Even a one or two minute break could be the pause that really refreshes.
Also, as you get more skilled in answering questions and see more clearly what is going on in them, answering them will take less effort and you will be less fatigued.
Another thing that you could try is working to achieve better flow and effortlessness while taking the test. Those topics are fairly extensive, but you could begin by taking a different attitude toward the test and noticing how you respond to it emotionally. Emotional responses can be tiring. Also, I have seen someone go from always getting fatigued to no longer getting fatigued just by changing her mindset.
