This paper presents a unified mathematical model of the hypothalamic–pituitary–adrenal (HPA) axis aiming to explore its dysfunction through the analysis of the circadian oscillations in the release of hormones in response to chronic and acute stressors. A comprehensive review of existing HPA simulation models reveals a lack of strong fit for validation datasets. To overcome these shortcomings, we have extended a minimal mechanistic model of the HPA axis by unifying a disrupted hormonal pathway between the hippocampus and hypothalamus, as well as a feedback loop of adrenocorticotropic hormone (ACTH) to control the release of corticotropin-releasing hormone (CRH). Additionally, we have integrated a disrupted hormonal pathway of the arginine vasopressin (AVP) to stimulate the pituitary gland to precisely release the ACTH, which altogether led to a significant reduction in the mean absolute percentage error as well as an improvement in the validation accuracy in the circadian release of cortisol and ACTH. This expansion enables to estimate model parameters to enhance predictive accuracy. Furthermore, through sensitivity and correlation analyses, we have identified parameters exerting the most significant influence on cortisol dynamics within the system, revealing intricate interdependencies among model components and within the HPA axis. Despite advancements, existing models are still lacking in addressing major factors such as genetic and epigenetic influences.