We investigate special orbital configurations of geometrically spaced three-planet systems. Lissauer and Gavino 2021 found that a significant fraction of compact three-planet systems has an anomalous lifetime that is several orders of magnitude larger than systems of similar orbital spacing. Some of these anomalous very compact systems remain stable for more than 10 billion years. Analysis shows that these stable systems 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 find that very specific initial orbital configurations lead to anomalous stability. In particular, We show that the initial phasing plays a fundamental role in stabilizing systems for timescales far larger than those of systems of similar orbital spacing. We then demonstrate that the analysis of the first few orbital revolutions can provide clues to know whether a system is anomalously long-lived or not.