Final answer:
The term for an unreasonable and sustained belief that a patient acknowledges may not be true when challenged is delusion.
Step-by-step explanation:
The term for an unreasonable and sustained belief that a patient acknowledges may not be true when challenged is delusion. Delusions are fixed, false beliefs that are not based on reality and are resistant to change even when presented with contradictory evidence. For example, a person with paranoid schizophrenia may have delusions of being constantly followed or persecuted, despite evidence to the contrary.