Communities often represent key structural and functional clusters in networks. To preserve such communities, it is important to understand their robustness under network perturbations. Previous work in community robustness analysis has focused on studying changes in the community structure as a response of edge rewiring and node or edge removal. However, the impact of increasing connectivity on the robustness of communities in networked systems is relatively unexplored. Studying the limits of community robustness under edge addition is crucial to better understanding the cases in which density expands or false edges erroneously appear. In this paper, we analyze the effect of edge addition on community robustness in synthetic and empirical temporal networks. We study two scenarios of edge addition: random and targeted. We use four community detection algorithms, Infomap, Label Propagation, Leiden, and Louvain, and demonstrate the results in community similarity metrics. The experiments on synthetic networks show that communities are more robust when the initial partition is stronger or the edge addition is random, and the experiments on empirical data also indicate that robustness performance can be affected by the community similarity metric. Overall, our results suggest that the communities identified by the different types of community detection algorithms exhibit different levels of robustness, and so the robustness of communities depends strongly on the choice of detection method.