Attack-Support Argumentation Framework (ASAF) is an extension of the Bipolar Argumentation Framework that allows for attacks and supports not only between arguments but also targeting attacks and supports at any level. In this paper we propose an incremental approach for computing the skeptical preferred acceptance in dynamic ASAFs. Specifically, we investigate how the skeptical acceptance of a goal element (an argument, an attack, or a support) evolves when a given ASAF is updated by adding or retracting an argument, an attack, or a support, and propose an incremental algorithm for solving this problem. Our approach relies on identifying a portion of the given ASAF which is sufficient to determine the status of the goal w.r.t. the updated ASAF. We experimentally evaluate our approach showing that it outperforms the computation from scratch on average.