There have been a number of protocols proposed for anonymous network communication. In this paper we investigate attacks by corrupt group members that degrade the anonymity of each protocol over time. We prove that when a particular initiator continues communication with a particular responder across path reformations, existing protocols are subject to the attack. We use this result to place an upper bound on how long existing protocols, including Crowds, Onion Routing, Hordes, Web Mixes, and DC-Net, can maintain anonymity in the face of the attacks described. Our results show that fully-connected DC-Net is the most resilient to these attacks, but it suffers from scalability issues that keep anonymity group sizes small. Additionally, we show how violating an assumption of the attack allows malicious users to setup other participants to falsely appear to be the initiator of a connection.