  We investigate the long-time limit of quantum localization of the kicked
Rydberg atom. The kicked Rydberg atom is shown to possess in addition to the
quantum localization time $\tau_L$ a second cross-over time $t_D$ where quantum
dynamics diverges from classical dynamics towards increased instability. The
quantum localization is shown to vanish as either the strength of the kicks at
fixed principal quantum number or the quantum number at fixed kick strength
increases. The survival probability as a function of frequency in the transient
localization regime $\tau_L<t<t_D$ is characterized by highly irregular,
fractal-like fluctuations.
