The long-term stability of microbiomes is crucial as the persistent occurrence of beneficial microbes and their associated functions ensure host health and well-being. Microbiomes are highly diverse and dynamic, making them challenging to understand. Because many natural systems work as temporal networks, we present an approach that allows identifying meaningful ecological patterns within complex microbiomes: the dynamic core microbiome. On the basis of six marine sponge species sampled monthly over three years, we study the structure, dynamics and stability of their microbiomes. What emerge for each microbiome is a negative relationship between temporal variability and mean abundance. The notion of the dynamic core microbiome allowed us to determine a relevant functional attribute of the microbiome: temporal stability is not determined by the diversity of a host's microbial assemblages, but rather by the density of those microbes that conform its core microbiome. The core microbial interaction network consisted of complementary members interacting weakly with dominance of comensal and amensal interactions that suggests self-regulation as a key determinant of the temporal stability of the microbiome. These interactions have likely coevolved to maintain host functionality and fitness over ecological, and even evolutionary time scales.