AI-generated text now constitutes a substantial and growing fraction of indexed web content, creating a feedback loop in which AI assistants may retrieve and condition on their own prior generations. Prior work shows that recursive training on model generations causes model collapse: a loss of output diversity and distributional drift. We ask whether a similar collapse emerges at inference time, when LLMs retrieve their own generations via RAG without any parameter updates. We measure collapse as the progressive convergence of responses to a narrow set across recursive retrieval rounds. Across three contamination simulations and four open-source LLMs, answer collapse is rapid and consistent under direct contamination, but slower, partial, and model-dependent under realistic competitive retrieval. Collapse can also degrade downstream accuracy on factual multi-hop QA, though the effect is inconsistent across models. We further show that the self-generated documents we introduce are cited far above their share of the retrieved context, an effect that is not fully explained by document quality, writing style, AI authorship, and self-preference. Finally, we propose and evaluate mitigation strategies at both the retrieval and generation stages, none of which reliably prevent collapse. As AI-generated content continues to populate the open web, collapse-resistant retrieval design becomes a prerequisite for trustworthy AI assistants.