Scalability is a critical challenge for blockchain-based cryptocurrencies. Payment channel networks (PCNs) have emerged as a promising solution for this challenge. However, channel balance depletion can significantly limit the capacity and usability of a PCN. Specifically, frequent transactions that result in unbalanced payment flows from two ends of a channel can quickly deplete the balance on one end, thus blocking future payments from that direction. In this paper, we propose Fence, an online balance-aware fee setting algorithm to prevent channel depletion and improve PCN sustainability and long-term throughput. In our algorithm, PCN routers set transaction fees based on the current balance and level of congestion on each channel, in order to incentivize payment senders to utilize paths with more balance and less congestion. Our algorithm is guided by online competitive algorithm design, and achieves an asymptotically tight competitive ratio with constant violation in a unidirectional PCN. We further prove that no online algorithm can achieve a finite competitive ratio in a general PCN. Extensive simulations under a real-world PCN topology show that Fence achieves high throughput and keeps network channels balanced, compared to state-of-the-art PCN routing algorithms.