  We consider a stationary and ergodic random field $\{\omega(e) : e \in E_d\}$
that is parameterized by the edge set of the Euclidean lattice $\mathbb{Z}^d$,
$d \geq 2$. The random variable $\omega(e)$, taking values in $[0, \infty)$ and
satisfying certain moment bounds, is thought of as the conductance of the edge
$e$. Assuming that the set of edges with positive conductances give rise to a
unique infinite cluster $\mathcal{C}_{\infty}(\omega)$, we prove a quenched
invariance principle for the continuous-time random walk among random
conductances under relatively mild conditions on the structure of the infinite
cluster. An essential ingredient of our proof is a new anchored relative
isoperimetric inequality.
