Safety alignment in large language models is remarkably shallow: it is concentrated in the first few output tokens and reversible by fine-tuning on as few as 100 adversarial examples. This fragility becomes critical in real-world deployment, where models undergo sequential adaptation across domains such as medicine, law, and code, causing safety guardrails to erode cumulatively. Yet all existing safety-preserving methods target only single-task fine-tuning, leaving the multi-domain sequential setting entirely unaddressed. We introduce SafeAnchor, a framework that anchors safety in place throughout continual adaptation. SafeAnchor first identifies low-rank safety subspaces in LoRA parameter space via Fisher Information eigendecomposition, then constrains domain-specific gradient updates to the orthogonal complement of these subspaces, and finally monitors for residual safety drift with threshold-triggered corrective replay. Evaluated on Llama-2-7B-Chat and Mistral-7B-Instruct across a three-domain pipeline and eight benchmarks, SafeAnchor retains 93.2% of original safety alignment, outperforming all baselines by 18-42 points, while matching unconstrained fine-tuning to within 1.5 points on domain tasks.