What condition involves permanent intellectual impairment that cannot be treated with medications?

The condition that involves permanent intellectual impairment that cannot be treated with medications is best categorized as a cognitive disorder. Cognitive disorders refer specifically to conditions that primarily affect cognitive functions such as memory, perception, problem-solving, and other intellectual capabilities. These impairments are often irreversible and not responsive to pharmacological treatments.

In contrast, mental illnesses can encompass a broader range of psychological and emotional disturbances, and many of them can be treated with medications. Neurological disorders typically involve the nervous system, affecting movement, coordination, and sensation, and while they may result in cognitive impairment, they are not exclusively focused on intellectual functioning. Emotional disturbances generally relate to conditions that affect mood and emotional regulation, which again can be treated with various therapies, including medication. Therefore, cognitive disorder is the most appropriate choice for the condition described in the question.