We present ReflexBench, the first benchmark designed to evaluate reflexive reasoning in large language models - the capacity to reason about one's own causal impact on the environment being analyzed. ReflexBench comprises 20 scenarios across 6 domains, each probing four levels of Observer Depth (OD). We evaluate 5 frontier LLMs and find that all exhibit systematic degradation at higher observer depths (mean Delta = -0.50). We propose the Soros Test as a practical standard for evaluating observer-participant readiness and document that reflexive capabilities emerge through a phase transition during multi-reward GRPO training.