Final answer:
Burnout is the term used to describe a prolonged state of mental and physical exhaustion that cannot be fixed by getting a good night's sleep.
Step-by-step explanation:
The term used to describe a prolonged state of mental and physical exhaustion that cannot be fixed by getting a good night's sleep is burnout. Burnout is a state of emotional, physical, and mental exhaustion caused by excessive and prolonged stress. It is often associated with chronic work-related stress and can lead to reduced productivity, cynicism, and detachment from work and personal life.