For reliable deployment of deep-learning systems, out-of-distribution (OOD) detection is indispensable. In the real world, where test-time inputs often arrive as streaming mixtures of in-distribution (ID) and OOD samples under evolving covariate shifts, OOD samples are domain-constrained and bounded by the environment, and both ID and OOD are jointly affected by the same covariate factors. Existing methods typically assume a stationary ID distribution, but this assumption breaks down in such settings, leading to severe performance degradation. We empirically discover that, even under covariate shift, covariate-shifted ID (csID) and OOD (csOOD) samples remain separable along a discriminative axis in feature space. Building on this observation, we propose DART, a test-time, online OOD detection method that dynamically tracks dual prototypes -- one for ID and the other for OOD -- to recover the drifting discriminative axis, augmented with multi-layer fusion and flip correction for robustness. Extensive experiments on a wide range of challenging benchmarks, where all datasets are subjected to 15 common corruption types at severity level 5, demonstrate that our method significantly improves performance, yielding 15.32 percentage points (pp) AUROC gain and 49.15 pp FPR@95TPR reduction on ImageNet-C vs. Textures-C compared to established baselines. These results highlight the potential of the test-time discriminative axis tracking for dependable OOD detection in dynamically changing environments.