Problem: I would like to clone a post from one site in my multisite network into another site in the same network using the WP Multisite Content Copier Pro plugin. This plugin allows me to clone a post across sites and was working as expected, but recently stopped working.
Solution: In this case exposing the custom fields to the REST API seems to have solved the problem. Manage that setting in Toolset > Settings > Custom Content. Check the checkbox for "Expose custom fields managed by Types for posts, users, and terms through the REST API" and save the settings.