Final answer:
An agency relationship may be terminated by various reasons, except for the principal's refusal of an offer to purchase made in the name of a third party.
Step-by-step explanation:
An agency relationship may be terminated by various reasons, but not all of the options provided. Among the options given, the only one that does not result in the termination of the agency relationship is the principal's refusal of an offer to purchase that was presented in the name of a third party. This is because the agency relationship is not directly affected by this action, but rather the purchase offer. The other options mentioned - a fire destroying the property, mutual agreement of principal and agent, and the renunciation of the agency by the agent - can all lead to the termination of the agency relationship.