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.
