Graph neural networks (GNNs) are increasingly widely used for community detection in attributed networks. They combine structural topology with node attributes through message passing and pooling. However, their robustness or lack of thereof with respect to different perturbations and targeted attacks in conjunction with community detection tasks is not well understood. To shed light into latent mechanisms behind GNN sensitivity on community detection tasks, we conduct a systematic computational evaluation of six widely adopted GNN architectures: GCN, GAT, Graph-SAGE, DiffPool, MinCUT, and DMoN. The analysis covers three perturbation categories: node attribute manipulations, edge topology distortions, and adversarial attacks. We use element-centric similarity as the evaluation metric on synthetic benchmarks and real-world citation networks. Our findings indicate that supervised GNNs tend to achieve higher baseline accuracy, while unsupervised methods, particularly DMoN, maintain stronger resilience under targeted and adversarial perturbations. Furthermore, robustness appears to be strongly influenced by community strength, with well-defined communities reducing performance loss. Across all models, node attribute perturbations associated with targeted edge deletions and shift in attribute distributions tend to cause the largest degradation in community recovery. These findings highlight important trade-offs between accuracy and robustness in GNN-based community detection and offer new insights into selecting architectures resilient to noise and adversarial attacks.