  Flatbands feature the distortion-free storage of compact localized states of
tailorable shape. Their reliable storage sojourn is, however, limited by
disorder potentials, which generically cause uncontrolled coupling into
dispersive bands. We find that, while detuning flatband states from band
intersections suppresses their direct decay into dispersive bands,
disorder-induced state distortion causes a delayed, dephasing-mediated decay,
lifting the static nature of flatband states and setting a finite lifetime for
the reliable storage sojourn. We exemplify this generic, disorder-induced decay
mechanism at the cross-stitch lattice. Our analysis, which applies
platform-independently, relies on the time-resolved treatment of
disorder-averaged quantum systems with quantum master equations.
