Hello Allison,
When a relationship class is created between two objects (tables, feature classes, etc.) you want to make sure that the user (viewer/editor) has permissions to view/edit BOTH the objects. It is not required to revoke and regrant permissions to the objects to be able to access them if sufficient privileges are applied to begin with.
I do notice, however, that you may be at an unsupported version of SQL Server for ArcGIS 10.6.1. The minimum supported SQL Server database for ArcGIS 10.6.1 is SQL Server 2012 SP3. Strange behaviors are commonly seen when unsupported versions are used, so it could be a possible cause of the issue you are seeing.
For your reference, I have listed below documentation that highlights the Microsoft SQL Server database requirements for ArcGIS 10.6.x:
https://desktop.arcgis.com/en/system-requirements/10.6/database-requirements-sqlserver.htm
I hope this helps!
Thanks,
Afreen