Final answer:
Ataxia is the term that describes loss of balance due to a brainstem or cerebellar injury, affecting voluntary movement coordination and potentially arising from various causes.
Step-by-step explanation:
The term used to describe loss of balance in a patient with a brainstem or cerebellar injury is ataxia. Ataxia involves a loss of coordination in voluntary movements and can be a result of damage to the cerebellum, leading to difficulty with balance and gait disorders. This condition can be caused by multiple factors including focal lesions, genetic disorders, or exposure to exogenous substances, impacting the cerebellum and its pathways. A thorough neurological exam, particularly the cranial nerve exam and balance and posture assessments, is critical in identifying the presence of ataxia.