The uptake of high penetrations of renewable energy in microgrids is curtailed by concerns that their intermittency may cause the system to become unstable. The classic approach of small-signal stability analysis may lead to overly optimistic conclusions, because it implicitly assumes that the intermittency is small-signal in nature. Instead, LMI techniques from robust controls can be used to provide large-signal stability guarantees that overcome this limitation. In this paper, we give an illustrative example of a microgrid that is guaranteed to be stable under small-signal intermittency, and show that it can be made unstable when the intermittency becomes large-signal. Instead, we compute more conservative large-signal stability margins using Lyapunov analysis, and show that the small- and large-signal stability margins are related by the maximum allowable slew-rate of the intermittency.