This paper presents a real-time fault-tolerant guidance method, which solves the autonomous rescue problem in the event of thrust drop failure during the final stage flight of launch vehicles. The core of the method is the online and optimal reconstruction of both the degraded target orbit and the subsequent flight trajectory. Aiming at achieving satisfied onboard computing performance and making the best use of the launcher’s residual energy, a unique relaxation-penalization model transformation method for the nonlinear orbit injection conditions is proposed, and a successive convexification algorithm is developed to solve the problem. Furthermore, both the two classic thrust drop failure situations, that is the mass flow rate drop and the specific impulse drop problems, can be resolved by the proposed algorithm. The average run-time of this orbit-trajectory joint optimization algorithm is below 150ms in an embedded ARM processor @1.5 GHz, which is adequate for onboard use. Using the above algorithm as a central infrastructure, a receding-horizon-strategy-based fault-tolerant guidance method is proposed. By performing the optimization repeatedly at a high frequency, the effects of parameter deviations and external disturbances can be absorbed for the most part, for example, the guidance algorithm is verified to be capable of tolerating at least ±5% thrust deviations. Comprehensive numerical and hardware-in-the-loop simulations are performed to demonstrate the computational performance, accuracy, and reliability of the proposed algorithms.