In this paper, we present a new agent-based and network-based model of protest campaigns in the presence of repression from the authorities. It includes both rational and socio-psychological factors in the behavior of the protesters. An analytical study of the simplified form of the model (without a network structure) leads to two main findings. First, a protest campaign unfolds successfully, reaching a significant number of participants, only if it overcomes a certain turnout threshold before the start of repression. Second, there exists a critical level of repression's severity, at which the protest campaign will not survive, regardless of the initial number of participants. This threshold occurs when individuals have a relatively high level of risk aversion. A computational experiment has shown that its existence and value do not depend on the network topologies, traditionally explored in the literature - namely Watts-Strogatz, Barabási-Albert, and regular graph. Yet an experiment has also demonstrated that this “repression barrier” can be overcome by more specialized network structures. One of them is the special version of the so-called STAR topology, when the most active and the only agent is linked with all other agents, allows the protest campaign to survive at any rate of repression.