Stability analysis is one of the key challenges in the design of large linear analog circuits with complex multi-loop structures. In this paper, we present an efficient loop finder algorithm to identify potentially unstable loops in such circuits. At the heart of our automated stability checker lie two newly developed computationally efficient algorithms --- the first to detect all poles within a given region of interest and the second to extract second order approximations of node impedance transfer functions given these pole locations. It is shown that the proposed technique outperforms existing stability methods by more than one order of magnitude for medium sized circuits and enables stability analysis of large extracted industrial designs which was previously infeasible.