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We investigate the radial stability of neutron stars under conditions where their composition may or may not remain in chemical equilibrium during oscillations. Using different equations of state that include nucleons, hyperons, and/or $\Delta$ resonances, we compute stellar configurations and examine their fundamental mode frequencies in two limiting scenarios. In one limit, nuclear reactions are fast enough to maintain chemical equilibrium throughout the pulsation, resulting in a lower effective adiabatic index, $\Gamma_{\mathrm{EQ}}$, and softer stellar responses. In the opposite limit, nuclear reactions are too slow to adjust particle abundances during oscillations, yielding a higher index, $\Gamma_{\mathrm{FR}}$, and stiffer stellar responses. We find that the equilibrium scenario triggers dynamic instability at the maximum mass configuration, whereas the frozen composition scenario allows stable solutions to persist beyond this mass, extending the stable branch. This effect is modest for simpler equations of state, but becomes increasingly pronounced for more complex compositions, where the emergence of new particle species at high densities leads to a significant disparity between $\Gamma_{\mathrm{EQ}}$ and $\Gamma_{\mathrm{FR}}$. Realistic conditions, in which different nuclear reactions have distinct timescales, will place the effective $\Gamma$ between these two extreme values. Short-timescale reactions push the star toward the equilibrium limit, potentially restricting the length of the stable branch. Conversely, slow reactions preserve a frozen composition, allowing the stable branch to grow. Thus, the actual extent of the stable configuration range depends critically on the interplay between nuclear-reaction timescales and the star's fundamental oscillation period., Comment: 20 pages, 3 figures