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Existing unlearning methods, however, are designed for single-step deletion and collapse after only 3-5 sequential applications. We trace this instability to two compounding factors: (i) coarse mapping targets that cause degradation to accumulate unnecessarily across steps, and (ii) the absence of local protection for semantically neighboring concepts, whose shared internal representations make them the first to suffer collateral damage. Because this damage is strongest in the local semantic neighborhood of the forget concept, global replay alone cannot prevent it. Building on this analysis, we propose Locality-Aware Continual Unlearning (LACU), a framework with two complementary mechanisms. 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Because this damage is strongest in the local semantic neighborhood of the forget concept, global replay alone cannot prevent it. Building on this analysis, we propose Locality-Aware Continual Unlearning (LACU), a framework with two complementary mechanisms. 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