Assumption-based argumentation (ABA) is a central structured argumentation\nformalism. As shown recently, answer set programming (ASP) enables efficiently\nsolving NP-hard reasoning tasks of ABA in practice, in particular in the\ncommonly studied logic programming fragment of ABA. In this work, we harness\nrecent advances in incremental ASP solving for developing effective algorithms\nfor reasoning tasks in the logic programming fragment of ABA that are\npresumably hard for the second level of the polynomial hierarchy, including\nskeptical reasoning under preferred semantics as well as preferential\nreasoning. In particular, we develop non-trivial counterexample-guided\nabstraction refinement procedures based on incremental ASP solving for these\ntasks. We also show empirically that the procedures are significantly more\neffective than previously proposed algorithms for the tasks.\n This paper is under consideration for acceptance in TPLP.\n