  The flow of quantum information in local dephasing channels is analyzed over
short and long times in case the structured reservoirs of frequency modes
exhibit a spectral gap in the density of modes over low frequencies. The
presence of the low-frequency gap with upper cut-off frequency $\omega_g$
produces over the time scale $1/\omega_g$ an infinite sequence of time
intervals over which information backflow appears. Such time intervals are
generally irregular but, under certain conditions, exhibit the following
bounds: the $n$th backflow has certainly started at the instant $\pi
\left(1+2(n-1)\right)/\omega_g$, and certainly ended at the instant $2\pi
n/\omega_g$, for every $n=1,2,\ldots$. The intervals become regular over long
times, tend to the asymptotic length $\pi/\omega_g$ as supremum value, and are
described analytically in terms of the structure of the spectral density near
the cut-off frequency. Consequently, engineering structured reservoirs of
frequency modes with low-frequency spectral gaps produces in local dephasing
channels regular and controllable sequences of information backflow and
recoherence over long times, along with non-Markovian evolution.
