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In this work, we conduct a comprehensive empirical study to understand why this setting remains difficult. A natural hypothesis is that failures stem from content access; yet across twelve retrieval, reflection, and verification baselines on CL-Bench, an extensive context learning benchmark, we find limited gains over direct full-context prompting. Further failure analysis reveals a key finding: unlike typical long-context tasks such as long document understanding, context learning requires not only recovering local content but also acquiring local specifications that are often unspecified in the query but distributed across the context: domain-specific formats, local rules, and completeness conditions. 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Further failure analysis reveals a key finding: unlike typical long-context tasks such as long document understanding, context learning requires not only recovering local content but also acquiring local specifications that are often unspecified in the query but distributed across the context: domain-specific formats, local rules, and completeness conditions. 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