Burnout
Burnout is not generally a mental issue (nor is it usually simple). The term suggests that the autonomic nervous system (ANS), which kicks into sympathetic gear in response to stress, has gone beyond its ability to respond anymore; literally the adrenals are burned out. Absolutely certainly you want to make sure that the client is taking some B-vitamin complexes (since cortisol burns up B vitamins), and it’s worth checking to see about the status of the adrenals, since there are some pretty good adrenal rescue supplements available that can help rebuild that part of the system.
In addition to high alpha amplitudes and poor alpha blocking, it is important to see whether the alpha is slow. It is very common to see this pattern in clients who have not dealt with emotional issues, rather keeping them buried (or wrapped in alpha) over a long period of time. The burnout could well be related to adrenal failure, which occurs when the autonomic nervous system has been in sympathetic mode over a long period of time. Often we see problems where the unprocessed emotional material gets somaticized, and it may appear as chronic fatigue, chronic pain or even fibromyalgia.
If the alpha is slow, below 10Hz, at the back of the head, you might try training faster alpha up at P4 with eyes closed. If you are using Brain-Trainer software, you can use the Alpha Up design to do this. If not, try training 2-9 Hz down and 10-13 Hz up.