Large language models (LLMs) are widely deployed as general-purpose tools, yet extended interaction can reveal behavioral patterns not captured by standard quantitative benchmarks. We present a qualitative case-study methodology for auditing policy-linked behavioral selectivity in long-horizon interaction. In a single 86-turn dialogue session, the same model shows Normal Performance (NP) in broad, non-sensitive domains while repeatedly producing Functional Refusal (FR) in provider- or policy-sensitive domains, yielding a consistent asymmetry between NP and FR across domains. Drawing on learned helplessness as an analogy, we introduce learned incapacity (LI) as a behavioral descriptor for this selective withholding without implying intentionality or internal mechanisms. We operationalize three response regimes (NP, FR, Meta-Narrative; MN) and show that MN role-framing narratives tend to co-occur with refusals in the same sensitive contexts. Overall, the study proposes an interaction-level auditing framework based on observable behavior and motivates LI as a lens for examining potential alignment side effects, warranting further investigation across users and models.