  The $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry protected topological (SPT)
phase hosts a robust boundary qubit at zero temperature. At finite energy
density, the SPT phase is destroyed and bulk observables equilibrate in finite
time. Nevertheless, we predict parametric regimes in which the boundary qubit
survives to arbitrarily high temperature, with an exponentially longer
coherence time than that of the thermal bulk degrees of freedom. In a dual
picture, the persistence of the qubit stems from the inability of the bulk to
absorb the virtual $\mathbb{Z}_2 \times \mathbb{Z}_2$ domain walls emitted by
the edge during the relaxation process. We confirm the long coherence time by
exact diagonalization and connect it to the presence of a pair of conjugate
almost strong zero modes. Our results provide a route to experimentally
construct long-lived coherent boundary qubits at infinite temperature in
disorder-free systems.
