This paper describes the study of a powered-coast-powered guidance reconfiguration (PCPGR) method used to solve the autonomous rescue problem for the mission profile of a launch vehicle with a coasting phase when the thrust drop fault occurs in the first powered phase (FPP) of the final stage. We first described the constraints of the final stage and the construction of the PCP guidance problem. Then we evaluated the adaptability of the guidance reconfiguration (GR) offline with numerical optimization by adjusting the constraints of the FPP, the coast phase, and the second powered phase. To determine the fault state set where the rocket can enter the prescribed target orbit through the GR initiate, we proposed a Newton method-based rapid replanning method of the transfer orbit that transforms the complex multi-flight phase trajectory planning problem into a feasible transfer orbit search problem to produce a fast solution onboard. Combined with the adaptive adjustment of the coasting time and the iterative guidance mode, we realized the autonomous online rescue of the payload. The simulation results showed that the proposed method achieved a reliable and rapid solution and improved a launch vehicle’s adaptability to a thrust drop fault.