Sybil attacks present a significant threat to many Internet systems and applications, in which a single adversary inserts multiple colluding identities in the system to compromise its security and privacy. Recent work has advocated the use of social-network-based trust relationships to defend against Sybil attacks. However, most of the prior security analyses of such systems examine only the case of social networks at a single instant in time. In practice, social network connections change over time, and attackers can also cause limited changes to the networks. In this work, we focus on the temporal dynamics of a variety of social-network-based Sybil defenses. We describe and examine the effect of novel attacks based on: (a) the attacker's ability to modify Sybil-controlled parts of the social-network graph, (b) his ability to change the connections that his Sybil identities maintain to honest users, and (c) taking advantage of the regular dynamics of connections forming and breaking in the honest part of the social network. We find that against some defenses meant to be fully distributed, such as SybilLimit and Persea, the attacker can make dramatic gains over time and greatly undermine the security guarantees of the system. Even against centrally controlled Sybil defenses, the attacker can eventually evade detection (e.g. against SybilInfer and SybilRank) or create denial-of-service conditions (e.g. against Ostra and SumUp). After analysis and simulation of these attacks using both synthetic and real-world social network topologies, we describe possible defense strategies and the trade-offs that should be explored. It is clear from our findings that temporal dynamics need to be accounted for in Sybil defense or else the attacker will be able to undermine the system in unexpected and possibly dangerous ways.