SLMs are increasingly deployed on devices, yet real-world prompts often contain textual or ASR noise that can destabilize model predictions. We analyze this problem from a token-level perspective and find that SLMs exhibit narrow logit margins between the gold token and the top-ranked non-gold token, making noisy prompts more likely to induce local rank flips. To address this issue, we propose LoMaR, a two-stage parameter-efficient framework for robust fine-tuning. In Stage I, LoMaR trains the model on clean prompts with a local logit margin expansion objective to expand the local decision boundary. In Stage II, LoMaR performs residual-subspace adaptation with local logit margin alignment on noisy prompts. After training, the main and residual updates are merged into a standard LoRA adapter, introducing no additional inference cost. Experimental results show that LoMaR outperforms baselines in most noisy settings and achieves lower Performance Drop Rate and Rank Flip Rate. Code and datasets are available at https://github.com/HongJin2828/LoMaR.