Custom column data is not archived in report & report_archive database in batch_instance table.
Each db in Ephesoft has its own purpose and is designed as per requirements. Report db is used to keep only those records which are used in generating reports. As custom columns have no use in report and flowing unnecessary records may slow down the etl process, so these custom columns were never introduced in batch_instance table of report db. Also report_archive is used to keep back up of report db, so these columns are also not present in batch_instance table of report_archive db.
You can write custom sql procedure or script / logic to move these details in some other table / database through in which you can keep a track of the data in custom columns.