A dataset is confounded if it is most easily solved via a spurious correlation which fails to generalize to new data. We will show that, in a continual learning setting where confounders may vary in time across tasks, the resulting challenge far exceeds the standard forgetting problem normally considered. In particular, we derive mathematically the effect of such confounders on the space of valid joint solutions to sets of confounded tasks. Interestingly, our theory predicts that for many such continual datasets, spurious correlations are easily ignored when the tasks are trained on jointly, but it is far harder to avoid confounding when they are considered sequentially. We construct such a dataset and demonstrate empirically that standard continual learning methods fail to ignore confounders, while training jointly on all tasks is successful. Our continually confounded dataset, ConCon, is based on CLEVR images and demonstrates the need for continual learning methods with more robust behavior with respect to confounding.