A decade of rapid advances in artificial intelligence (AI) has opened new opportunities for clinical decision support systems (CDSS), with large language models (LLMs) demonstrating strong reasoning abilities on timely medical tasks. However, clinical texts are often degraded by human errors or failures in automated pipelines, raising concerns about the reliability and fairness of AI-assisted decision-making. Yet the impact of such degradations remains under-investigated, particularly regarding how noise-induced shifts can heighten predictive uncertainty and unevenly affect demographic subgroups. We present a systematic study of state-of-the-art LLMs under diverse text corruption scenarios, focusing on robustness and equity in next-visit diagnosis prediction. To address the challenge posed by the large diagnostic label space, we introduce a clinically grounded label-reduction scheme and a hierarchical chain-of-thought (CoT) strategy that emulates clinicians' reasoning. Our approach improves robustness and reduces subgroup instability under degraded inputs, advancing the reliable use of LLMs in CDSS. We release code at https://github.com/heejkoo9/NECHOv3.