Intelligent lower-limb exoskeleton rehabilitation robots are increasingly superseding traditional rehabilitation equipment, making them a focus of research in this field. However, existing systems remain challenged by dynamic instability resulting from various disturbances during actual walking. To address this limitation, this study proposes a novel dynamic stability criterion. Through an analysis of the principles and limitations of the traditional zero-moment point (ZMP) stability criterion, particularly during the late single-leg support phase, a new stability criterion is introduced, which is founded on the swing projection polygon during single-leg support. This approach elucidates the variation patterns of the stability polygon during a single-step motion and facilitates a qualitative analysis of the stability characteristics of the human–robot system in multiple postures. To further enhance the stability and smoothness of gait trajectories in lower-limb exoskeleton rehabilitation robots, the shortcomings of conventional gait planning approaches, namely their non-intuitive nature and discontinuity, are addressed. A recurrent gait planning method leveraging Long Short-Term Memory (LSTM) neural networks is proposed. The integration of the periodic motion characteristics of human gait serves to validate the feasibility and correctness of the proposed method. Finally, based on the recurrent gait planning method, the dynamic stability of walking postures is verified through theoretical analysis and experimental comparisons, accompanied by an in-depth analysis of key factors influencing dynamic stability.