Engine, the indispensable core of a rocket, has a significant impact on space exploration, especially the high-thrust liquid-propellant rocket engine. Most new-generation manned rockets for space stations or lunar exploration prefer the engine for its high performance and environmental friendliness. However, the engine is susceptible to failure under extreme conditions, which could cause catastrophic consequences without timely warning. Real-time state detection and fault location can prevent some catastrophic outcomes, but they require reliable sensor data. Nevertheless, some sensor data could be lost due to signal interruptions or equipment shutdown caused by system faults. Therefore, recovering the lost data based on the remaining measurements is a critical challenge that involves dealing with the distribution gap between normal and faulty data. To tackle the data drift and achieve real-time and high-precision sensor data recovery of the faulty engine, a multistage model based on graph convolutional networks is proposed in this paper. Trained by a multiloss function, the model primarily recognizes the status of the engine and passes the status to the next stage. Then the second stage recovers the lost data by two graph convolutional networks specific to the normal or faulty state. Evaluated on the practical experimental data from Xi’an Aerospace Propulsion Institute, our method successfully identifies the state of the system with accuracy above 99.99% and recovers the incomplete sensor data with a mean absolute error under 0.0065. Moreover, some ablation studies demonstrate that the blocks of two-stage and graph convolution could achieve a 26% improvement over the vanilla neural network.