Save Our Rural Health Providers Act This bill requires a specific portion of the Public Health and Social Services Emergency Fund to be allocated to rural health care providers responding to COVID-19 (i.e., coronavirus disease 2019). Specifically, the bill requires that at least 20% of future appropriations and the unobligated balance of prior appropriations to the fund relating to COVID-19 provider assistance be reserved for rural health care providers, with priority given to providers serving a high number of Medicare or Medicaid enrollees, elderly or other high-risk individuals, uninsured individuals, or areas with limited health infrastructure.