  We study the zero-temperature stochastic Ising model on some connected planar
quasi-transitive graphs, which are invariant under rotation and translation.
The initial spin configuration is distributed according to a Bernoulli product
measure with parameter $ p\in(0,1) $. In particular, we prove that if $ p=1/2 $
and the graph underlying the model satisfies the planar shrink property (which
causes each finite cluster to shrink to a site and then vanish with positive
probability) then all vertices flip infinitely often almost surely.
