The storage effect is a general explanation for ecological coexistence, wherein different species specialize on different states of a fluctuating environment, e.g., hot vs. cold years. Despite the storage effect's prominence in theoretical ecology, we lack evidence on whether it maintains biodiversity in nature. Here, we examine five storage effects in a community of 11 coral species from the Great Barrier Reef, using detailed size-structured demographic data collected over five years. We parameterize integral projection models, simulate coral communities, and quantify coexistence mechanisms through Modern Coexistence Theory. Results show that storage effects promote coexistence but are weak compared to fitness differences. Despite coral communities exhibiting theoretical prerequisites for strong temporal niche partitioning, the storage effect plays only a minor role in maintaining coral biodiversity. This aligns with growing evidence that storage effects are weak across ecosystems. Coral coexistence likely depends more on spatial processes, including microhabitat partitioning and asymmetric dispersal.