I'm putting this here even though I have a ticket open, as a means of documenting this. Admins, I'm not posting here to hurry you up, rather just for future reference and for others.
The environment to replicate the bug is.
Create custom field that is available for members ONLY (not billing), and is NOT an "All Events" field
Create event that has group registration
Enable the field on the event for members only (not billing).
Register for the event and the data entered for the field is NOT stored.