  We iteratively apply a recently formulated adiabatic theorem for the
strong-coupling limit in finite-dimensional quantum systems. This allows us to
improve approximations to a perturbed dynamics, beyond the standard
approximation based on quantum Zeno dynamics and adiabatic elimination. The
effective generators describing the approximate evolutions are endowed with the
same block structure as the unperturbed part of the generator, and exhibit
adiabatic evolutions. This iterative adiabatic theorem reveals that
adiabaticity holds eternally, that is, the system evolves within each
eigenspace of the unperturbed part of the generator, with an error bounded by
$O(1/\gamma)$ uniformly in time, where $\gamma$ characterizes the strength of
the unperturbed part of the generator. We prove that the iterative adiabatic
theorem reproduces Bloch's perturbation theory in the unitary case, and is
therefore a full generalization to open systems. We furthermore prove the
equivalence of the Schrieffer-Wolff and des Cloiseaux approaches in the unitary
case and generalize both to arbitrary open systems, showing that they share the
eternal adiabaticity, and providing explicit error bounds. Finally we discuss
the physical structure of the effective adiabatic generators and show that
ideal effective generators for open systems do not exist in general.
