The deployment of specialized language models in resource-constrained edge environments ( $\le 1$B parameters, $\le 2$ GB memory, $\le 100$ ms latency) faces a critical challenge: Supervised Fine-Tuning (SFT) achieves domain expertise but suffers from irreversible catastrophic forgetting, while traditional Low-Rank Adaptation (LoRA) with conservative ranks ( $r\le 64$) often underperforms due to insufficient adaptation capacity. This work introduces H-LoRA (High-Rank LoRA) for edge-deployable models and establishes a fundamental distinction between destructive forgetting and controllable knowledge retention. Through comprehensive experiments on compact models ( $0.12$B Minimind and Qwen- $0.5$B) across three domains (Human Resources, Medical, Mathematics) using 29,647 samples, we demonstrate that while both SFT and H-LoRA exhibit general capability degradation, they differ fundamentally: SFT completely destroys the original knowledge structure ( $1\mathrm{\%}$ topic retention), while H-LoRA maintains knowledge integrity with $90\mathrm{\%}$ topic retention—an $89$ percentage point improvement—enabling post-deployment capability recovery. H-LoRA employs simplified scaling and strategic high-rank adaptation at approximately two-thirds of the model’s hidden dimension ( $r=512$ for $d=768$), achieving SFT-level domain performance ( $99.81\mathrm{\%}$ precision) with $5\times$ greater parameter efficiency ( $20.35\mathrm{\%}$ trainable parameters) and robust cross-domain generalization ( $93.5\pm 6.8\mathrm{\%}$ average precision). In addition, H-LoRA reduces over-the-air (OTA) update size from $1.4$ GB to $96$ MB ( $\approx 93\mathrm{\%}$), enabling practical and frequent deployment of specialized models in bandwidth-limited edge environments. Beyond demonstrating effectiveness, this work establishes the first comprehensive framework for characterizing specialization-retention trade-offs in parameter-efficient fine-tuning, providing practical guidance for method selection in real-world deployments.