People persist in mistaken beliefs even in settings with high stakes, abundant data, and repeated opportunities to learn—settings where standard arguments imply they should correct their errors. We develop an attention-based framework for understanding why errors persist. When a person channels his attention through the lens of his potentially misspecified model, exposure to data is not the same as tracking the statistics necessary to tell him his model is wrong. A model is attentionally stable when the data the person deems relevant fail, in the long run, to make the model look implausible. Models that erroneously rule things out—e.g., beliefs that a variable doesn’t matter or that a distinction doesn’t exist—tend to be attentionally stable because they divert attention away from data that would refute the model. Conversely, models that erroneously rule things in are less likely to be stable. Whether an error is discovered depends on the structure of the decision problem but is not tightly linked to its stakes; arbitrarily costly errors can persist while trivially inexpensive ones may be detected. Nevertheless, no error is robust both to changes in the decision environment and to shocks that expand attention: every channeled-attention error is vulnerable to some perturbation that would reveal it. We use the framework to analyze the stability of psychological biases and empirical misconceptions, as well as to explain why fresh eyes catch mistakes, why people use overly coarse rather than overly fine categorizations, and why people recognize errors in others that they miss in themselves.