We address the average-consensus problem for a distributed system whose components (nodes) can exchange information via unreliable interconnections (edges) that form an arbitrary, possibly directed topology (digraph). We consider a general setting where heterogeneous communication links may drop packets with generally unequal probabilities, independently between different links. We develop a distributed linear-iterative algorithm in which nodes maintain and update certain values based on the corresponding values they successfully receive from their in-neighbors. We demonstrate that, even when communication links drop packets with unequal probabilities, the proposed algorithm allows nodes to asymptotically reach average-consensus almost surely, as long as the underlying (possibly directed) communication topology forms a strongly connected digraph. Additionally, we provide a bound on the algorithm convergence rate.