Post-Acute Infection Syndromes (PAIS) are medical conditions that persist following acute infections from pathogens such as SARS-CoV-2, Epstein-Barr virus, and Influenza virus. Despite growing global awareness of PAIS and the exponential increase in biomedical literature, only a small fraction of this literature pertains specifically to PAIS, making the identification of pathogen-disease associations within such a vast, heterogeneous, and unstructured corpus a significant challenge for researchers. This study evaluated the effectiveness of large language models (LLMs) in extracting these associations through a binary classification task using a curated dataset of 1,000 manually labeled PubMed abstracts. We benchmarked a wide range of open-source LLMs of varying sizes (4B-70B parameters), including generalist, reasoning, and biomedical-specific models. We also investigated the extent to which prompting strategies such as zero-shot, few-shot, and Chain of Thought (CoT) methods can improve classification performance. Our results indicate that model performance varied by size, architecture, and prompting strategy. Zero-shot prompting produced the most reliable results, with Mistral-Small-Instruct-2409 and Nemotron-70B achieving strong balanced accuracy scores of 0.81 and macro F1 scores of up to 0.80, while maintaining minimal invalid outputs. While few-shot and CoT prompting often degraded performance in generalist models, reasoning models such as DeepSeek-R1-Distill-Llama-70B and QwQ-32B demonstrated improved accuracy and consistency when provided with additional context.