Magnetohydrodynamic computation demonstrates that feedback can sustain reversal and reduce the loop voltage in resistive shell reversed field pinch (RFP) plasmas. Edge feedback on approximately 2R/a tearing modes resonant near the axis is found to restore plasma parameters to nearly their levels obtained with a close fitting conducting shell. When original dynamo modes are stabilized, neighbouring tearing modes grow to maintain the RFP dynamo more efficiently. This suggests that the experimentally observed limits on RFP pulse lengths to the order of the shell time can be overcome by applying feedback to a few helical modes