Though there has been an extensive body of work on efficiently solving computational problems for static Dung's argumentation frameworks (AFs), little work has been done for handling dynamic AFs and in particular for deciding the skeptical acceptance of a given argument. In this paper we devise an efficient algorithm for computing the skeptical preferred acceptance in dynamic AFs. More specifically, we investigate how the skeptical acceptance of an argument (goal) evolves when the given AF is updated and propose an efficient algorithm for solving this problem. Our algorithm, called SPA, relies on two main ideas: i) computing a small portion of the input AF, called "context-based" AF, which is sufficient to determine the status of the goal in the updated AF, and ii) incrementally computing the ideal extension to further restrict the context-based AF. We experimentally show that SPA significantly outperforms the computation from scratch, and that the overhead of incrementally maintaining the ideal extension pays off as it speeds up the computation.