Given the cost and critical functions of satellite constellations, ensuring mission longevity and safe decommissioning is essential for space sustainability. This article presents a Model Predictive Control for spacecraft trajectory and setpoint stabilization under multiple actuation failures. The proposed solution allows us to efficiently control the faulty spacecraft enabling safe navigation towards servicing or collision-free trajectories. The proposed scheme ensures closed-loop asymptotic stability and is shown to be recursively feasible. We demonstrate its efficacy through open-source numerical results and realistic experiments using the ATMOS platform.