Repeated jumping is crucial to the mobility of jumping robots. In this paper, we extend upon the REBOund jumping robot design, an origami-inspired jumping robot that uses the Reconfigurable Expanding Bistable Origami (REBO) pattern as its body. The robot design takes advantage of the pattern's bistability to jump with controllable timing. For jump repeatedly, we also add self-righting legs that utilize a single motor actuation mechanism. We describe a dynamic model that captures the compression of the REBO pattern and the REBOund self-righting process and compared it to the physical robot. Our experiments show that the REBOund is able to successfully self-right and jump repeatedly over tens of jumps. Supplemental video: https://youtu.be/LoCXcwIxCgU