We propose a novel approach for enhancing depth videos containing non-rigidly deforming objects. Depth sensors are capable of capturing depth maps in real-time but suffer from high noise levels and low spatial resolutions. While solutions for reconstructing 3D details in static scenes, or scenes with rigid global motions have been recently proposed, handling unconstrained non-rigid deformations in relative complex scenes remains a challenge. Our solution consists in a recursive dynamic multi-frame super-resolution algorithm where the relative local 3D motions between consecutive frames are directly accounted for. We rely on the assumption that these 3D motions can be decoupled into lateral motions and radial displacements. This allows to perform a simple local per-pixel tracking where both depth measurements and deformations are dynamically optimized. The geometric smoothness is subsequently added using a multi-level L1 minimization with a bilateral total variation regularization. The performance of this method is thoroughly evaluated on both real and synthetic data. As compared to alternative approaches, the results show a clear improvement in reconstruction accuracy and in robustness to noise, to relative large non-rigid deformations, and to topological changes. Moreover, the proposed approach, implemented on a CPU, is shown to be computationally efficient and working in real-time.