Stress and depression are biological disorders. A study shows that excessive stress and severe depression can block new nerve connections in the brain and can disrupt circuits associated with mental functioning and emotions and consequently, shrink the brain.

The stress responses activate a region inside the brain known as the amygdala, which further sends a signal alerting the organism about the threat. As a result, the HPA (hypothalamic-pituitary-adrenal) gets activated and releases a flood of hormones, including cortisol, regarded as the “stress hormone” whose long-term exposure causes brain neurons to shrink.
Different type of stress affects different parts of the brain:
Recent life events, such as any traumatic accident or a job loss can directly affect our emotional awareness. As this part of the brain shrinks, we may start to lose control of our emotions and act in inappropriate ways.
Life traumas, such as living with a chronic condition such as cancer or losing a loved one can also affect our mood centers and may lead to depression and other mood disorders such as anxiety.
Over-secretion of stress hormones majorly affects our memory negatively. In particular, the hippocampus, prefrontal cortex and the amygdala are the parts of our brain that are affected.
All these brain disorders gradually lead to reduction in the volume of the brain. This has even been proved by various MRI studies conducted on the people suffering from chronic depression.
Understanding and managing the stress can inevitably be beneficial for a healthy and efficient working of the brain.
Reference (s):
https://www.psychologytoday.com/blog/the-mindful-self-express/201208/how-prevent-stress-shrinking-your-brain
http://www.dailymail.co.uk/health/article-2187592/How-stress-depression-shrink-brain.html