As multimodal content continues to expand at a rapid pace, audio retrieval has emerged as a key enabling technology for media search, content organization, and intelligent assistants. However, most existing benchmarks concentrate on semantic matching and fail to capture the fact that real-world queries often demand advanced reasoning abilities, including negation understanding, temporal ordering, concurrent event recognition, and duration discrimination. To address this gap, we introduce ReasonAudio, the first reasoning-intensive benchmark for Text-Audio Retrieval, comprising 1,000 queries and 10,000 composite audio clips across five fundamental reasoning tasks: Negation, Order, Overlap, Duration, and Mix. Despite their intuitive nature for humans and straightforward construction, these tasks pose significant challenges to current models. Our evaluation of ten state-of-the-art models reveals the following findings: All models struggle with reasoning-intensive audio retrieval, performing particularly poorly on Negation and Duration while showing relatively better results on Overlap and Order. Moreover, Multimodal Large Language Model-based embedding models fail to inherit the reasoning capabilities of their backbones through contrastive fine-tuning, suggesting that current training paradigms are insufficient to preserve reasoning capacity in retrieval settings