Logical vulnerabilities in software stem from flaws in program logic rather than memory safety, which can lead to critical security failures. Although existing automated program repair techniques primarily focus on repairing memory corruption vulnerabilities, they struggle with logical vulnerabilities because of their limited semantic understanding of the vulnerable code and its expected behavior. On the other hand, recent successes of large language models (LLMs) in understanding and repairing code are promising. However, no framework currently exists to analyze the capabilities and limitations of such techniques for logical vulnerabilities. We aim to systematically evaluate both traditional and LLM based repair approaches for addressing real world logical vulnerabilities. To facilitate our assessment, we created the first ever dataset, LogicDS, comprising 122 logical vulnerabilities that reflect tangible security impact. We also developed a systematic framework, LogicEval, to evaluate patches for logical vulnerabilities. Evaluations suggest that compilation and testing failures are primarily driven by prompt sensitivity, loss of code context, and difficulty in patch localization.