Final answer:
Duncan refused to sing at the National Theatre due to a series of unfortunate events that made him lose trust in people and the place.
Step-by-step explanation:
Duncan refused to sing at the National Theatre because he had a series of unfortunate events and experiences that made him lose trust in people and in the place itself. His behavior and boasting about his money made the neighbors resentful, and his secretary betrayed his trust by stealing money and securities. This loss, along with the betrayal of confidence, made Duncan feel that the place had cost him his belief in human nature. Therefore, he decided not to sing at the National Theatre.