Pups for Patriots Act of 2017 This bill directs the Department of Veterans Affairs (VA) to carry out a pilot program under which it shall enter into contracts with qualified nonprofit organizations to provide service dogs to eligible veterans who: served on active duty in the Armed Forces on or after September 11, 2001, have been diagnosed with severe or extreme post-traumatic stress or with a severe traumatic brain injury by a VA doctor or clinical social worker, have received evidence-based treatment and remains symptomatic of severe or extreme post-traumatic stress or severe traumatic brain injury, and commit to an evaluation by a VA doctor or social worker at least twice a year. A qualified nonprofit organization is a nonprofit organization that adheres to prescribed national standards for the selection, training, and assessment of service dogs for veterans. Such program must also furnish veterinary insurance for each such service dog. The VA shall issue to a veteran to whom a service dog is provided a national service dog credential if the veteran furnishes certain documents to the VA.