  We use perturbation theory to construct a family of time-dependent
microstrata: a set of non-extremal solutions of IIB supergravity asymptotic to
$AdS_3 \times S^3 \times T^4$. Our construction shows that the "special locus"
constraints of arXiv:2307.13021 can be broken by allowing the solutions to
depend on time. We study the secular terms appearing in the perturbation
theory. Some of them can be resummed into frequency shifts, with the same
interpretation as for the previously-studied microstrata solutions. Other
secular terms appear harder to resum, questioning the long-term stability of
the solutions.
