Length of Service Award Program Cap Adjustment Priority Act or the LOSAP CAP Act This bill amends the Internal Revenue Code, with respect to deferred compensation plans, to increase the limit on accruals that is required for length of service award plans (LOSAPs) for bona fide volunteers to be exempt from treatment as a deferred compensation plan. (Under current law, plans paying solely length of service awards to bona fide volunteers or their beneficiaries on the account of firefighting and prevention services, emergency medical services, and ambulance services performed by the volunteers are not treated as deferred compensation plans if they meet certain requirements. One of the requirements is a limit on the aggregate amount of length of service awards that may accrue with respect to any year of service for any bona fide volunteer.) The bill modifies the limit on accruals to: (1) increase the limit from $3,000 to $6,000; (2) provide for a cost-of-living adjustment to the limit after 2017; and (3) specify that, in the case of LOSAPs that are defined benefit plans, the limit applies to the actuarial present value of the aggregate amount of length of service awards accruing with respect to any year of service.