Custom fields not saving on network sites

I’m using CustomPress to create a custom post type with custom fields. In the editor, everything is showing up correctly (aside from the custom fields label as addressed in another thread). On the main site on the network, if I fill out the custom fields and publish, everything is saved. If I do the same thing on one of the network sites, the custom fields aren’t saved. I’ve tried deactivating all of the site-specific plugins and going back to the default theme, neither of which helps.

WP 3.3.2