In this paper we investigate forgetting notions in general, possibly non-flat assumption-based argumentation (ABA) frameworks. Research on forgetting is driven by desiderata the operators should adhere to. We consider two forgetting desiderata, called persistence and elimination and study under which ABA semantics they can be satisfied. Striving to keep our study as generic as possible, we derive our results in an abstract argumentation formalism called bipolar SETAFs (BSAFs) which capture non-flat ABA. Thereby, we consider different sub-classes which results in a broad study of the matter. Due to the close correspondence between ABA and BSAFs, we can transfer our findings to non-flat ABA. Our investigation reveals that in most cases, persistence cannot be satisfied by any forgetting operator, while elimination can be achieved most of the time.