The paper introduces a new approach to modeling Internet shutdown during the process of protest mobilization. The central point of the approach is the sequential use of two networks, with different topologies built upon the same set of individuals. Some endogenously set proportion of connections is shared by both networks. A model of protest dynamics is built on the developed approach. Numerical experiments with the model show that the effect of shutdown depends crucially on the degree of anger that triggers the protest campaign. This anger may arise, for example, from contested elections or an act of unjustified repression. The inference from the numerical experiments is that shutdown basically stifles protest activity if the triggering anger is high, and fuels protest activity if the triggering anger is low.