Registering an object shape to a sequence of point clouds undergoing non-rigid deformation is a long-standing challenge. The key difficulties stem from two factors: (i) the presence of local minima due to the non-convexity of registration objectives, especially under noisy or partial inputs, which hinders accurate and robust deformation estimation, and (ii) error accumulation over long sequences, leading to tracking failures. To address these challenges, we introduce to adopt a scalable data-driven approach and propose ERNet, an efficient feed-forward model trained on large deformation datasets. It is designed to handle noisy and partial inputs while effectively leveraging temporal information for accurate and consistent sequential registration. The key to our design is predicting a sequence of deformation graphs through a two-stage pipeline, which first estimates frame-wise coarse graph nodes for robust initialization, before refining their trajectories over time in a sliding-window fashion. Extensive experiments show that our proposed approach (i) outperforms previous state-of-the-art on both the DeformingThings4D and D-FAUST datasets, and (ii) achieves more than 4x speedup compared to the previous best, offering significant efficiency improvement.