A popular version of anti-Humeanism is one that views fundamental properties as being irreducibly dispositional in nature, and it is a view to which I am attracted. Proponents of this view typically object to Humean regularity theories of laws on the basis that they do not explain why our world is regular rather than chaotic from moment to moment. It is thought that, for this reason, Humeanism does not provide firm enough foundations for induction. However, in this paper I argue that it is far from clear how these anti-Humeans can themselves explain this regularity. This is because it is far from clear how they can explain why the entities in our world do not change their dispositional properties arbitrarily over time. This is a neglected problem, which I call the retention problem. In an attempt to solve this problem, several naturalistic explanations of retention are explored. Unfortunately, none of these explanations is free of problems, showing that dispositional forms of anti-Humeanism may not have as many advantages as some have assumed where the problem of induction is concerned.