Many studies explore how people 'come into' misinformation exposure. But much less is known about how people 'come out of' misinformation exposure. Do people organically sever ties to misinformation spreaders? And what predicts doing so? Over six months, we tracked the frequency and predictors of ~900K followers unfollowing ~5K health misinformation spreaders on Twitter. We found that misinformation ties are persistent. Monthly unfollowing rates are just 0.52%. In other words, 99.5% of misinformation ties persist each month. Users are also 31% more likely to unfollow non-misinformation spreaders than they are to unfollow misinformation spreaders. Although generally infrequent, the factors most associated with unfollowing misinformation spreaders are (1) redundancy and (2) ideology. First, users initially following many spreaders, or who follow spreaders that tweet often, are most likely to unfollow later. Second, liberals are more likely to unfollow than conservatives. Overall, we observe a strong persistence of misinformation ties. The fact that users rarely unfollow misinformation spreaders suggests a need for external nudges and the importance of preventing exposure from arising in the first place.