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We examine the scenario in which a mobile network of robots must search, survey, or cover an environment and communication is restricted by relative location. While many algorithms choose to maintain a connected network at all times while performing such tasks, we relax this requirement and examine the use of periodic connectivity, where the network must regain connectivity at a fixed interval. We propose an online algorithm that scales linearly in the number of robots and allows for arbitrary periodic connectivity constraints. To complement the proposed algorithm, we provide theoretical inapproximability results for connectivity-constrained planning. Finally, we validate our approach in the coordinated search domain in simulation and in real-world experiments.