Symbolic clinical natural language processing (NLP) systems remain widely used for extracting clinical concepts from electronic health record (EHR) narratives, but maintaining rule resources requires extensive manual error analysis and rule refinement. This study investigates whether large language models (LLMs) can assist in identifying extraction errors and generating candidate rules to improve symbolic clinical NLP systems. Using error reports derived from a multi-site evaluation of a previously validated symbolic model for cognitive and neuropsychiatric-related clinical concepts, we developed a human-in-the-loop framework, REFINE. The framework first uses LLMs to classify extraction errors and generate explanatory reasoning, which can then be incorporated into prompts for rule generation. Three LLMs (GPT-5.2, GPT-4o, GPT-4o-mini) were evaluated under four prompting conditions. LLM-generated rule sets improved performance compared with the baseline NLP-CAM system, increasing F1-score from 0.37 to 0.58. These findings suggest that LLMs can support scalable rule refinement for symbolic clinical NLP systems.