Credit networks rely on decentralized, pairwise trust relationships (channels) to exchange money or goods. Credit networks arise naturally in many financial systems, including the recent construct of payment channel networks in blockchain systems. An important performance metric for these networks is their transaction throughput. However, predicting the throughput of a credit network is nontrivial. Unlike traditional communication channels, credit channels can become imbalanced; they are unable to support more transactions in a given direction once the credit limit has been reached. This potential for imbalance creates a complex dependency between a network's throughput and its topology, path choices, and the credit balances (state) on every channel. Even worse, certain combinations of these factors can lead the credit network to deadlocked states where no transactions can make progress. In this paper, we study the relationship between the throughput of a credit network and its topology and credit state. We show that the presence of deadlocks completely characterizes a network's throughput sensitivity to different credit states. Although we show that identifying deadlocks in an arbitrary topology is NP-hard, we propose a peeling algorithm inspired by decoding algorithms for erasure codes that upper bounds the severity of the deadlock. We use the peeling algorithm as a tool to compare the performance of different topologies as well as to aid in the synthesis of topologies robust to deadlocks.