Saving Rural Hospitals from Closure Act This bill modifies requirements for the Medicare Accelerated and Advance Payment Program during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019). The program provides Medicare payments in advance to eligible providers experiencing claims or cash flow disruptions, such as during national emergencies; the program was specifically expanded in response to COVID-19 to encompass more types of providers, subject to certain recoupment and repayment provisions. The bill allows the Centers for Medicare & Medicaid Services to forgive repayment, extend the recoupment timeline, and lower applicable interest rates for hospitals experiencing significant financial hardship (e.g., impending bankruptcy).