Arc-avoidance conjecture for supereulerian semicomplete digraphs

Let $D=(V,A)$ be a $(k+1)$-arc-strong semicomplete digraph, meaning that $D$ remains strongly connected after deletion of any set of at most $k$ arcs. Let $A'\subset A$ be any set of $k$ arcs.

Arc-avoidance conjecture. The digraph $D\setminus A'$ is supereulerian.

This is the arc-connectivity analogue of the Fraisse–Thomassen theorem for hamiltonian cycles in tournaments. The source does not state whether this conjecture has been resolved.