Driven by sustainability and economic considerations, two-sided recommendation platforms are required to satisfy the needs of both users and providers. Previous studies often indicate that the two sides' needs differ in urgency: providers have relatively long-term exposure requirements, while users desire short-term, accurate services. However, our empirical study reveals that existing methods for balancing fairness and accuracy often fail to ensure both long-term fairness and short-term accuracy under fluctuating user traffic in real applications. Notably, when user traffic is low, user experience tends to decline significantly. Then, we conducted a theoretical analysis confirming that user traffic is a crucial factor in such a trade-off problem. Ensuring accuracy and fairness under variable user traffic remains a challenge. Inspired by the bankruptcy problem in economics, we propose a novel fairness-aware re-ranking approach called BankFair. BankFair intuitively uses the Talmud rule to leverage periods of high user traffic to compensate for periods of low traffic, ensuring consistent user service while maintaining long-term fairness. BankFair is composed of two modules: (1) utilizing the Talmud rule to determine the necessary degree of fairness across varying user traffic periods, and (2) implementing an online re-ranking algorithm based on the fairness degree established by the Talmud rule. Experiments on one publicly available and one real industrial dataset demonstrate that BankFair outperforms all baselines in terms of both accuracy and provider fairness.