Large language model (LLM) coding agents, such as Claude Code, are increasingly used for security auditing, with task-specific skills providing reusable vulnerability-analysis procedures. However, their effectiveness in detecting real vulnerabilities and the reasons for their failures remain unclear. We conduct the first large-scale empirical study of 37 security skills using Claude Code with four underlying LLMs on 100 real Linux kernel vulnerabilities across ten classes, totaling 14800 runs. We evaluate vulnerability detection at the function, statement, and vulnerability-class levels. Results show that 24.4 percent of runs locate the correct function, 18.3 percent identify both the function and responsible statement, and 15.7 percent correctly classify the vulnerability. Our failure analysis reveals limitations in evidence acquisition, state-relation reasoning, code interpretation, candidate verification, investigation coverage, and reporting. Based on these findings, we propose SKILL-SIF, a self-improving framework that iteratively evolves security skills by learning from missed vulnerabilities and failure patterns. We evolve five top-performing skills using the original benchmark and evaluate them on 100 previously unseen vulnerabilities. SKILL-SIF improves fully correct vulnerability detection by up to eight times (from 2 percent to 16 percent) on unseen vulnerabilities, while aggregate accuracy across four LLMs increases by 1.85 times (from 6.05 percent to 11.20 percent). These findings highlight the limitations of existing security skills and demonstrate the potential of failure-driven skill evolution to improve vulnerability detection in coding agents.

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