With respect to the special case of eclipses concerning the Earth-Moon-Sun system: Because the lunar orbit is determined by three periodicities of the lunar orbit, each with different periods, so a set eclipse "cycle" can only repeat itself after an (roughly) integer number of synodic, draconic, and anomalistic months. read more
The additional dimming in brightness events, called the tertiary and quaternary eclipses, reappeared at irregular intervals of time, indicating the stars were in different positions in their orbit each time the third body passed. read more