Given a directed graph $G=(V,A)$, capacity and cost functions on $A$, a root $r$, a subset $T \subset V$ of terminals, and an integer $k$, we aim at selecting a minimum cost subset $A'\subseteq A$ such that for every subgraph of $G'=(V,A')$ obtained by removing $k$ arcs from $A'$ it is possible to route one unit of flow from $r$ to each terminal while respecting the capacity constraints. We focus on the case where the input graph $G$ is planar and propose a tabu search algorithm whose main procedure takes advantage of planar graph duality properties.