If a group of custom fields is configured for Activities - when you add or edit an activity record and enter a value - the value is not saved.
You can try this out on the sandbox - adding an Interview activity type for this contact:
I also tested locally with a custom data group that was NOT for a specific Activity Type - but was Used For = Activities ... Any. Same results, the value didn't save.
In both tests, one of the custom field types was Yes/No - although I'm not sure if that's significant.