Gas hydrates are one of the largest marine carbon reservoirs on Earth. The conventional understanding of hydrate dynamics assumes that the system converges to a steady-state over geological time-scales, achieving fixed concentrations of gas hydrate and free gas phase. However, using a high-fidelity numerical model and consistently resolving phase states across multiple fluid-fluid and fluid-solid phase boundaries, we have identified well-defined periodic states embedded within hydrate system dynamics. These states lead to cyclic formation and dissolution of massive hydrate layers that is self-sustaining even in the absence of external triggers. This previously unresolved characteristic could manifest as spontaneous gas discharge and pressure release in, supposedly, unperturbed systems. Our findings challenge the foundational principle that the gas hydrate systems have unique steady-state solutions. Instead, existence of periodic states introduces an irreducible uncertainty in gas hydrate dynamics which puts significant error bars on previous hydrate estimates.