This paper presents a method to design robust trajectories against the possible faults of low-thrust engines. Recently, increasing number of space probes with low-thrust engines have been developed. Due to the insufficient reliability of low-thrust propulsion system, almost all probes with ion engines have experienced the failure of engines. Conventional methods to design the low-thrust trajectory have pursued fuel minimum solution to only one target celestial body which does not necessarily mean the maximization of mission achievement. In other words, it can enhance the mission accomplishment to intelligently change the trajectory when engine failures occur. In this research, the objective function is defined as expected scientific gain, and the optimal solution is searched by a proposed method. Resulting method, Bellman Rapidly-exploring Random Trees (Bellman RRT) are efficiently extended by applying the Bellman equation. Finally, the numerical simulation demonstrated that the Bellman RRT improved the mission achievement using real deep space exploration scenario.