Interpretability plays a vital role in aligning and deploying deep learning models in critical care, especially in constantly evolving conditions that influence patient survival. However, common interpretability algorithms face unique challenges when applied to dynamic prediction tasks, where patient trajectories evolve over time. Gradient, Occlusion, and Permutation-based methods often struggle with time-varying target dependency and temporal smoothness. This work systematically analyzes these failure modes and supports learnable mask-based interpretability frameworks as alternatives, which can incorporate temporal continuity and label consistency constraints to learn feature importance over time. Here, we propose that learnable mask-based approaches for dynamic timeseries prediction problems provide more reliable and consistent interpretations for applications in critical care and similar domains.