Truth discovery networks evaluate the trustworthiness of sources (e.g., websites) and their claims (e.g., the severity of a virus). Intuitively, the more trustworthy the sources of a claim, the more believable the claim and vice versa. Singleton noted that bipolar abstract argumentation could be a natural way to reason about these networks. We explain how this idea can be implemented naturally by quantitative bipolar argumentation frameworks (QBAFs) that we call TD-QBAFs. While most applications of QBAFs result in a (nearly) acyclic structure, TD-QBAFs have bi-directional edges and can feature complex cycles. The stability (convergence behaviour) of QBAFs in cyclic graphs is currently not well understood. While pathological examples of divergent QBAFs have been constructed, the problems seemed unlikely to occur in practice. However, convergence problems seem to be the rule rather than the exception for TD-QBAFs. We demonstrate how common QBAF semantics can fail to converge for very simple TD-QBAFs and discuss some of the potential causes. While this shows limitations of existing semantics, we also discuss how some previously proposed ideas can be used to mitigate the problems and demonstrate their effectiveness empirically.