BMI has no expiration rule, but a termination rule, though it
seems that this rule is not enforced:
Members who have not recorded any activity with bmi, its diamond club partners, or made a redemption with the same parties and other promotional third parties, for a 12 month period, from the date of their last recorded activity on the diamond club database, shall be deemed dormant. If no claim is made on any residual Destination Miles on that member's account, membership may be terminated after a further 12 months and all remaining miles forfaited.
It translates into 2 years after the last activity, if it was enforced.