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Imbalanced token distributions naturally exist in text documents, leading neural language models to overfit on frequent tokens. The token imbalance may dampen the robustness of radiology report generators, as complex medical terms appear less frequently but reflect more medical information. In this study, we demonstrate how current state-of-the-art models fail to generate infrequent tokens on two standard benchmark datasets (IU X-RAY and MIMIC-CXR) of radiology report generation. To solve the challenge, we propose the \textbf{T}oken \textbf{Im}balance Adapt\textbf{er} (\textit{TIMER}), aiming to improve generation robustness on infrequent tokens. The model automatically leverages token imbalance by an unlikelihood loss and dynamically optimizes generation processes to augment infrequent tokens. We compare our approach with multiple state-of-the-art methods on the two benchmarks. Experiments demonstrate the effectiveness of our approach in enhancing model robustness overall and infrequent tokens. Our ablation analysis shows that our reinforcement learning method has a major effect in adapting token imbalance for radiology report generation.