Well, it worked for almost a year, and there has been no changes recently that can explain the error. No plugins have been added for weeks, and there were no updates made around the time the error occured. It worked. Then it didn't….
I've solved it by simply using a new field group for new posts. If I use both field groups however, the data in the old fields will be imported into the new fields when I update the post. It's very strange. Disabling plugins and/or switching the theme is not an option due to the high profile and traffic on this website.
Thanks anyway though.