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Model Predictive Control (MPC), which involves online optimization of a receding-horizon objective, has been effectively used to generate robust and reactive controllers for many problem domains. For tasks involving extreme nonlinearities such as contact, the use of warm-starts, which are essential for efficient optimization, quickly drive the predicted trajectory into bad local minima, leading to failure. In this paper we present a principled method for avoiding this mode of failure, by combining offline trajectory optimization and online MPC, generating robust controllers for complex periodic behavior in domains with contact. We first find an optimal limitcycle offline, and compute a local quadratic approximation of the infinite-horizon Value function around it. We then use this approximation as the terminal cost for the online MPC optimizer. This combination of an offline solution of the infinite-horizon problem with an online MPC controller is known as Infinite Horizon Model Predictive Control (IHMPC), and we show how under certain conditions it can generate the infinite-horizon optimal behavior using finite-horizon optimization. Finally, we present a simulation of a hopping robot controlled by IHMPC. The resulting behavior is robust against simulated perturbations and modeling errors.