Reversed field pinch (RFP) sustainment is studied in the framework of three dimensional magnetohydrodynamic (MHD) numerical simulations. The scaling law for the magnetic fluctuation amplitude with Lundquist number S is delta B approximately=S-0.22, which can be understood if the basic dynamic processes are governed by current sheet reconnection. Quasi-periodic oscillations are in fact found to be correlated with the presence of localized sheet currents, which for sufficiently large S make the major contribution to the average power dissipated by fluctuations. Special attention is paid to numerical convergence in the simulations. The results are compared with experimental observations