We analyze 88 independent high-resolution cosmological zoom-in simulations of disk galaxies in the NIHAO simulations suite to explore the connection between the atomic gas fraction and angular momentum of baryons throughout cosmic time. The study is motivated by the analytic model of citet{obreschkow16}, which predicts a relation between the atomic gas fraction $f_{rm atm}$ and the global atomic stability parameter $q equiv jsigma / (GM)$, where $M$ and $j$ are the mass and specific angular momentum of the galaxy (stars+cold gas) and $sigma$ is the velocity dispersion of the atomic gas. We show that the simulated galaxies follow this relation from their formation ($zsimeq4$) to present within $sim 0.5$ dex. To explain this behavior, we explore the evolution of the local Toomre stability and find that $90%$--$100%$ of the atomic gas in all simulated galaxies is stable at any time. In other words, throughout the entire epoch of peak star formation until today, the timescale for accretion is longer than the timescale to reach equilibrium, thus resulting in a quasi-static equilibrium of atomic gas at any time. Hence, the evolution of $f_{rm atm}$ depends on the complex hierarchical growth history primarily via the evolution of $q$. An exception are galaxies subject to strong environmental effects.
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