Real-time guidance is critical for the vertical recovery of rockets. However, traditional sequential convex optimization algorithms suffer from shortcomings in terms of their poor real-time performance. This work focuses on applying the deep learning-based closed-loop guidance algorithm and error propagation analysis for powered landing, thereby significantly improving the real-time performance. First, a controller consisting of two deep neural networks is constructed to map the thrust direction and magnitude of the rocket according to the state variables. Thereafter, the analytical transition relationships between different uncertainty sources and the state propagation error in a single guidance period are analyzed by adopting linear covariance analysis. Finally, the accuracy of the proposed methods is verified via a comparison with the indirect method and Monte Carlo simulations. Compared with the traditional sequential convex optimization algorithm, our method reduces the computation time from 75 ms to less than 1 ms. Therefore, it shows potential for online applications.