Large language models (LLMs) increasingly require mechanisms for continual adaptation without full retraining. However, sequential updates can lead to catastrophic forgetting, where new edits degrade previously acquired knowledge. This work presents STABLE, a gated continual self editing framework that constrains forgetting during sequential updates using parameter efficient fine tuning via Low Rank Adaptation (LoRA; see arXiv:2106.09685). Each candidate edit is evaluated against a stability budget using one of three metrics: (i) Exact Match (EM) drop, capturing factual accuracy loss; (ii) bits increase, reflecting reduced model confidence; and (iii) KL divergence, quantifying distributional drift between the base and adapted models. If a threshold is exceeded, the LoRA update is rescaled through a clipping procedure or rejected. Experiments on the Qwen-2.5-7B model show that gating effectively mitigates forgetting while preserving adaptability. EM based gating achieved the highest cumulative performance in short continual learning sequences. Our results show that different gating strategies can achieve comparable distribution shift (measured by KL divergence) while producing different accuracy outcomes, highlighting the importance of gating design in continual adaptation. This approach offers a principled method for continual model editing, enabling LLMs to integrate new knowledge while maintaining reliability. Code: https://github.com/Bhoy1/STABLE