Persistent surveillance with aerial vehicles (drones) subject to connectivity and power constraints is a relatively uncharted domain of research. To reduce the complexity of multi-drone motion planning, most state-of-the-art solutions ignore network connectivity and assume unlimited battery power. Motivated by this and advances in optimization and constraint satisfaction techniques, we introduce a new persistent surveillance motion planning problem for multiple drones that incorporates connectivity and power consumption constraints. We use a recently developed constrained optimization tool (Satisfiability Modulo Convex Optimization (SMC)) that has the expressivity needed for this problem. We show how to express the new persistent surveillance problem in the SMC framework. Our analysis of the formulation based on a set of simulation experiments illustrates that we can generate the desired motion planning solution within a couple of minutes for small teams of drones (upto 5)