  We consider time-dependent random walks among time-dependent conductances.
For discrete time random walks, we show that, unlike the time-independent case,
two-sided Gaussian heat kernel estimates are not stable under perturbations.
This is proved by giving an example of a ballistic and transient time-dependent
random walk on Z among uniformly elliptic time-dependent conductances. For
continuous time random walks, we show the instability when the holding times
are i.i.d. exp(1), and in contrast, we prove the stability when the holding
times change by sites in such a way that the base measure is a uniform measure.
