A dataset is confounded if it is most easily solved via a spurious correlation, which fails to generalize to new data. In this work, we show that, in a continual learning setting where confounders may vary in time across tasks, the challenge of mitigating the effect of confounders far exceeds the standard forgetting problem normally considered. In particular, we provide a formal description of such continual confounders and identify that, in general, spurious correlations are easily ignored when training for all tasks jointly, but it is harder to avoid confounding when they are considered sequentially. These descriptions serve as a basis for constructing a novel CLEVR-based continually confounded dataset, which we term the ConCon dataset. Our evaluations demonstrate that standard continual learning methods fail to ignore the dataset's confounders. Overall, our work highlights the challenges of confounding factors, particularly in continual learning settings, and demonstrates the need for developing continual learning methods to robustly tackle these.