  We study the dynamics of periodically-kicked many-body systems away from the
high-frequency regime, and discuss a family of Floquet systems where the notion
of prethermalization can be naturally extended to intermediate and low driving
frequencies. We investigate numerically the dynamics of both integrable and
nonintegrable systems, and report on the formation of a long-lived prethermal
plateau, akin to the high-frequency limit, where the system thermalizes with
respect to an effective Hamiltonian captured by the inverse-frequency expansion
(IFE). Unlike the high-frequency regime, we find that the relevant heating
times are model dependent: we analyze the stability of the prethermal plateau
to small perturbations in the drive period, and show that, in a spin chain
whose IFE is intractable, the plateau duration is insensitive to the
perturbation strength, in contrast to a chain where the IFE admits the
resummation of an entire subseries. Infinitesimal perturbations are enough to
restore the ergodic properties of the system, and decrease residual finite-size
effects. Although the regime where the Floquet system leaves the prethermal
plateau and starts heating up to infinite temperature is not captured by the
IFE, we provide evidence that the evolved subsystem is described well by a
thermal state w.r.t.~the IFE Hamiltonian, with a gradually changing
temperature, in accord with the Eigenstate Thermalization Hypothesis.
