Teach and Repeat (T&R) topometric navigation enables robots to autonomously repeat previously traversed paths without relying on GPS, making it well suited for operations in GPS-denied environments such as underground mines and lunar navigation. State-of-the-art T&R systems typically rely on iterative closest point (ICP)-based estimation; however, in geometrically degenerate environments with sparsely structured terrain, ICP often becomes ill-conditioned, resulting in degraded localization and unreliable navigation performance. To address this challenge, we present a degeneracy-resilient Frequency-Modulated Continuous-Wave (FMCW) lidar T&R navigation system consisting of Doppler velocity-based odometry and degeneracy-aware scan-to-map localization. Leveraging FMCW lidar, which provides per-point radial velocity measurements via the Doppler effect, we extend a geometry-independent, correspondence-free motion estimation to include principled pose uncertainty estimation that remains stable in degenerate environments. We further propose a curvature-enhanced degeneracy-aware localization method that leverages per-point curvature for improved data association and adaptive registration formulation, and unifies translational and rotational scales to enable consistent degeneracy detection. Closed-loop field experiments spanning environments with varying structural richness demonstrate that the proposed system reliably completes autonomous navigation, including in a challenging flat airport test field where a conventional ICP-based system fails. We release the implementation of this work at: https://opensource_code/place_holder.

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