This paper studies the Cucker-Smale (C-S) flocking subject to random failure under general interaction topologies, which contain the hierarchical leadership and rooted leadership as special cases. Furthermore, at each time step, each of the agents can fail to interact with any of its neighbors. The random failures are assumed to be not independent. We prove that the flocking would occur almost surely under some conditions on the initial state of the flock only. The result suggests that the C-S flocking system on general digraphs can endure random failure in interactions. Finally, several numerical simulations are provided to illustrate the obtained results. (C) 2019 Elsevier Ltd. All rights reserved.