Sgt. Ketchum Rural Veterans Mental Health Act of 2021 This bill requires the Department of Veterans Affairs (VA), during FY2022, to establish and maintain three new centers of the Rural Access Network for Growth Enhancement (RANGE) Program in areas with interest from personnel and a need for additional mental health care for rural veterans. The RANGE Program serves veterans in rural areas who are experiencing mental illness. The bill requires the Government Accountability Office to conduct a study and report on whether the VA has sufficient resources to serve rural veterans who need mental health care that is more intensive than traditional outpatient therapy.