Which of the following is a classic sign of acute adrenal insufficiency?

Abdominal pain is indeed a classic sign of acute adrenal insufficiency. In cases of adrenal crisis, patients often present with abdominal pain, which can mimic an acute abdomen. This is due to the stress response and the resultant release of hormones, as well as potential electrolyte imbalances that can accompany adrenal insufficiency. The associated symptoms often arise from the body's inability to maintain homeostasis during times of severe stress or illness.

In contrast, the other choices do not typically align with the hallmark presentations of acute adrenal insufficiency. For instance, bluish-black discolorations of the mucous membranes are more commonly associated with conditions like acanthosis nigricans or other pigmentation disorders rather than adrenal insufficiency. Profound bradycardia is not a primary manifestation of adrenal crisis; rather, patients usually present with tachycardia due to cardiovascular instability. Severe headache can occur in numerous conditions but is not a classic sign specifically indicative of acute adrenal insufficiency. Therefore, abdominal pain stands out as a crucial symptom that aids in the identification of this medical emergency.