I checked the permission differences in each feature class within the feature dataset and they all have the same permissions - I also created a brand new feature dataset and then added a new feature class and still behaving the same.
Another difference that I spotted is:
The ones that are working are; outside of a feature dataset and look like this:
GISDB.PORT.TAXLOT_PORT
The ones that are not working are (1) within a feature datastet and (2) outside of a feature dataset. but look like this:
gisdb.PORT.lease_activedoco_join
So not sure if that is causing an issue for the MXD to reset back the SQL connection are the ones that are lowercase? We have not had ran into this issue before.