Prompt Tuning is a popular parameter-efficient finetuning method for pre-trained large language models (PLMs). Recently, based on experiments with RoBERTa, it has been suggested that Prompt Tuning activates specific neurons in the transformer's feed-forward networks, that are highly predictive and selective for the given task. In this paper, we study the robustness of Prompt Tuning in relation to these "skill neurons", using RoBERTa and T5. We show that prompts tuned for a specific task are transferable to tasks of the same type but are not very robust to adversarial data, with higher robustness for T5 than RoBERTa. At the same time, we replicate the existence of skill neurons in RoBERTa and further show that skill neurons also seem to exist in T5. Interestingly, the skill neurons of T5 determined on non-adversarial data are also among the most predictive neurons on the adversarial data, which is not the case for RoBERTa. We conclude that higher adversarial robustness may be related to a model's ability to activate the relevant skill neurons on adversarial data.