Exchanging the breaker to see if it is defective is a quick and easy way to eliminate that from the equation.
However, I agree with several of the above statements regarding the age of the equipment and it being the likely problem. 30 year old equipment will simply not be compatable with AFCI technology.
While it may not be practical or economically feasible to replace the entire fan assembly, you may be able to simply replace the motor and controller components.
