Protection and Advocacy for Veterans Act This bill directs the Department of Veterans Affairs (VA) to establish a five-year grant program to improve the monitoring of VA mental health and substance abuse treatment programs. The VA shall award a grant to four protection and advocacy systems under which each recipient shall investigate and monitor VA facilities care and treatment of veterans with mental illness or substance abuse issues. Criteria for selecting recipients shall include whether the state in which the protection and advocacy system operates has low mental health, performance, and access scores. During each year in which a protection and advocacy system carries out a demonstration project, the VA shall award a joint grant to a national organization with extensive knowledge of the protection and advocacy system and a veterans service organization to: (1) coordinate training and technical assistance, and (2) provide for related data collection, reporting, and analysis. "Protection and advocacy system" means the state-established system to protect and advocate the rights of persons with developmental disabilities.