Primary Aldosteronism: This condition is characterized by the excessive production of aldosterone, leading to hypertension that can be resistant to conventional antihypertensive therapy. The labile nature of the hypertension, along with refractoriness to treatment, makes primary aldosteronism a strong candidate for the single most likely diagnosis.

Pheochromocytoma: A catecholamine-secreting tumor that can cause episodic or sustained hypertension. The labile nature of the blood pressure is a hallmark of this condition, making it a likely diagnosis in patients with refractory hypertension.
Renal Artery Stenosis: Narrowing of the renal arteries can lead to renovascular hypertension, which may not respond well to standard antihypertensive medications. The mechanism involves activation of the renin-angiotensin-aldosterone system in response to decreased renal perfusion.

Cushing's Syndrome: Although less common, Cushing's syndrome due to excess cortisol can cause severe and refractory hypertension. Missing this diagnosis could lead to significant morbidity and mortality due to the systemic effects of excess cortisol.
Hyperthyroidism: Uncontrolled hyperthyroidism can lead to increased sympathetic activity, resulting in labile hypertension. This condition is critical not to miss due to the potential for serious cardiac and other systemic complications if left untreated.

Hyperparathyroidism: Rarely, primary hyperparathyroidism can lead to hypertension due to the effects of excess parathyroid hormone on calcium metabolism and vascular smooth muscle. While less common, it's an important consideration in refractory hypertension, especially if associated with hypercalcemia.
Coarctation of the Aorta: A congenital narrowing of the aortic isthmus, which can present in adulthood with refractory hypertension. Although rare, it's a critical diagnosis to consider due to the potential for serious complications, including aortic dissection and heart failure, if not addressed.