The issue of cyber-security has become ever more prevalent in the analysis and design of cyber-physical systems. In this paper, we investigate self-triggered consensus networks in the presence of communication failures caused by denial-of-service (DoS) attacks. A general framework is considered in which the network links can fail independent of each other. By introducing a notion of persistency-of-communication (PoC), we provide an explicit characterization of DoS frequency and duration under which consensus can be preserved by suitably designing time-varying control and communication policies. An explicit characterization of the effects of DoS on the consensus time is also provided. The considered notion of PoC is compared with classic ave...