We demonstrate so-called repetitive non-destructive readout (RNDR) for the first time on a single electron sensitive readout (SiSeRO) device. SiSeRO is a novel on-chip charge detector output stage for charge-coupled device image sensors, developed at MIT Lincoln Laboratory. This technology uses a p-MOSFET transistor with a depleted internal gate beneath the transistor channel. The transistor source-drain current is modulated by the transfer of charge into the internal gate. RNDR was realized by transferring the signal charge non-destructively between the internal gate and the summing well (SW), which is the last serial register. The advantage of the non-destructive charge transfer is that the signal charge for each pixel can be measured at the end of each transfer cycle, and by averaging for a large number of measurements (Ncycle), the total noise can be reduced by a factor of 1/Ncycle. In our experiments with a prototype SiSeRO device, we implemented nine (Ncycle=9) RNDR cycles, achieving around two electron readout noise (equivalent noise charge or ENC) with a spectral resolution close to the fano limit for silicon at 5.9 keV. These first results are extremely encouraging, demonstrating successful implementation of the RNDR technique in SiSeROs. They also lay the foundation for future experiments with more optimized test stands (better temperature control, larger number of RNDR cycles, and RNDR-optimized SiSeRO devices), which should be capable of achieving sub-electron noise sensitivities. This new device class presents an exciting technology for next generation astronomical X-ray telescopes requiring very low-noise spectroscopic imagers. The sub-electron sensitivity also adds the capability to conduct in-situ absolute calibration, enabling unprecedented characterization of the low energy instrument response.