We perform an in-depth study of the orbital dynamics of systems of three equal mass planets that are initially on geometrically spaced orbits. We explore a wide range of orbital spacings using numerical integrations for virtual times of up to 10 billion years or until the systems become unstable. Although the overall dependence of initial orbital spacing on lifetime is similar to that in analogous five-planet systems, we find that compact three-planet systems exhibit surprisingly very narrow space parameters where they are anomalously stable. It is notable that these regions are located far from strong mean motion resonances and far away from the separation beyond which systems are expected to be long-lived because three-body resonances do not overlap. We present an analysis of these anomalous regions and we show that differences in initial longitudes can have larger effects on lifetimes than differences in initial orbital separations. In particular, We find that early conjunctions play a major role in the angular momentum deficit evolution, which greatly affects the system lifetime.