Event custom fields not carried over to repeat events
This sure seems like an oversight on CiviCRM's part.  Good call for testing on the demo to rule out some weird problem on your site.

At this point, the bug needs to be reported and fixed.  Go to issues.civicrm.org and create an issue.  That way it can be triaged and assigned to the best person to fix it.

Unfortunately, until a fix comes out, you'll have to manually select the new recurring events in the custom data settings.