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Hilbert space fragmentation is an intriguing paradigm of ergodicity breaking
in interacting quantum many-body systems with applications to quantum
information technology, but it is usually adversely compromised in the presence
of perturbations. In this work, we demonstrate the protection of constrained
dynamics arising due to a combination of mirror symmetry and Hilbert space
fragmentation by employing the concept of quantum Zeno dynamics. We focus on an
Ising spin ladder with carefully chosen quantum fluctuations, which in the
ideal case guarantee a perfect disentanglement under Hamiltonian dynamics for a
large class of initial conditions. This is known to be a consequence of the
interplay of Hilbert space fragmentation with a mirror symmetry, and we show
numerically the effect of breaking the latter. To evince the power of this
perfect disentanglement, we study the effect of generic perturbations around
the fine-tuned model, and show that we can protect against the undesirable
growth of entanglement entropy by using a local Ising interaction on the rungs
of the ladder. This allows us to suppress the entanglement entropy to an
\textit{arbitrarily} small value for an \textit{arbitrarily} long time by
controlling the strength of the rung interaction. Our work demonstrates the
experimentally feasible viability of quantum Zeno dynamics in the protection of
quantum information against thermalization.