E-commerce search faces challenges such as sparse data and poor generalization from issues like multi-attribute resolution, multi-hop reasoning, and implicit intent. We propose iterative reranking as a compute-scaling strategy for LLM-based rankers, repeatedly applying listwise rankers to refine results by exploiting LLM non-determinism. Evaluated on three open datasets with three open-source LLMs, the method trades increased computation for consistently improved performance, yielding strong nDCG@40 gains on DL19, FutureQueryEval, and difficult Amazon query types. These findings show that iterative reranking is an effective inference-time scaling approach for LLM rankers. We make our code available ( https://github.com/amazon-science/IterativeListwiseReranking ).