Well, one thing to consider is that when you do practice tests, you take them to know how your progress is. If you have problems focusing during the verbal section, and thus you believe that it's a lost exam because it doesn't really show your actual progress (it's generally not a good idea to practice when you are tired), if your exams allow it, you can switch the order of the quant and verbal sections and alternated between them. For example: first practice exam: quant and then verbal; second exam: verbal then quant, and so on.
During your preparation period, if your schedule allows it, try to study in longer blocks of time, as much as possible. It's better to study for 4 hours at once than study 2 hours in the morning and 2 in the evening. Even when the time spent is the same, working 4 consecutive hours will build your stamina. If possible, never study less than 2 and a half hours (75 min + 75 min), since that is the length of both sections combined. So a lot of effort goes in scheduling your study time.
For full practice exams: try to learn the AWA template early in your preparation. Many people leave it for the last days. But I think that if you are used to it and want to build stamina and practice full length exams comparable to the real thing, then it's better to do the AWA in each test. That way, after some tests, you can focus on purposely setting your mind on spending minimal intellectual energy on the AWA section, kind of cruising through on an automatic pilot mode. This way, you get to the later sections with some fuel left in the tank.
Of course, you also need make a conscious effort to fight fatigue and lack of focus during your study and practice tests. That's the only way to increase stamina after some time.
I hope this tips will help you!