  Floquet spin chains have been a venue for understanding topological states of
matter that are qualitatively different from their static counterparts by, for
example, hosting $\pi$ edge modes that show stable period-doubled dynamics.
However the stability of these edge modes to interactions has traditionally
required the system to be many-body localized in order to suppress heating. In
contrast, here we show that even in the absence of disorder, and in the
presence of bulk heating, $\pi$ edge modes are long lived. Their lifetime is
extracted from exact diagonalization and is found to be non-perturbative in the
interaction strength. A tunneling estimate for the lifetime is obtained by
mapping the stroboscopic time-evolution to dynamics of a single particle in
Krylov subspace. In this subspace, the $\pi$ edge mode manifests as the
quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose
dimerization vanishes in the bulk of the Krylov chain.
