Entanglement sudden death (ESD) in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterization of classicality in Gaussian states, the time to ESD is calculated by analyzing the covariance matrices of the system. The results for the two-mode system at T = 0 and T > 0 for the two types of bath states are generalized to n modes, and are shown to be similar in nature to the results for the general discrete n-qubit system.