The hypothalamic-pituitary-adrenal (HPA) axis can be summarised in this diagram, with the hormones released at each level creating a negative feedback loop with the level above.
Image from Empowered Health Institute
Corticotrophin releasing hormone (CRH) from the hypothalamus stimulates the pituitary to produce adrenocorticotrophic hormone (ACTH), which in turn stimulates the adrenal gland (specifically its outer cortex) to produce glucocorticoids like cortisol.
The adrenal gland is made up of the cortex and medulla. The cortex produces steroid hormones including glucocorticoids, mineralocorticoids, and adrenal androgens, and the medulla produces the catecholamines, epinephrine, and norepinephrine.
ACTH is a growth factor for the adrenal cortex. The presence of exogenous glucocorticoids (such as prescribed steroids) will suppress ACTH production and eventually lead to adrenal atrophy.
It seems that a period of 4-6 weeks of insufficient ACTH will cause some degree of adrenal atrophy.
This is taken from Glucocorticoid Withdrawal—An Overview on When and How to Diagnose Adrenal Insufficiency in Clinical Practice:
A prolonged (more than 4–6 weeks) insufficient ACTH secretion leads to an atrophy of the zona fasciculata and reticularis and decreased ability to secrete cortisol.
In turn, it referenced the following chapter in a book, which I do not have full access to:
Carroll T.B., Aron D.C., Findling J.W., Tyrrell J.B. Glucocorticoids and Adrenal Androgens. In: Gardner D.G., Shoback D., editors. Greenspan’s Basic & Clinical Endocrinology. 10th ed. McGraw-Hill Education; New York, NY, USA: 2017.
During this period, a synthetic ACTH (“Synacthen test”) may yield a normal result as the adrenal gland can still respond.