With adrenal fatigue, Wilson suggests checking cortisol on a normal stressful day when one by definition is struggling. If you typically feel bottomed out at a certain time of day, make sure that one of the samples is from that time. One's cortisol should be dropping well before 11PM. However, if you are wide awake at the hour when you are wanting to be falling asleep, test then. Some have low cortisol levels and some have inverted patterns.
Otherwise Wilson suggests [page 85] 6-8 AM, within one hour of waking, 11-12AM, 4-6PM 10-12PM