This was working with earlier version of Publisher - seems to have happened after update to 3.9.1.
Have a channel that contains a grid field, which in turn contains a relationship field.
It appears I can only define one relationship entry - and only in the first row in the grid.
Relationships can be specified on other rows of the grid, but when entry is saved, these relationships are not saved.
I have found that I can manually over-ride this behaviour by adding entries manually to the table exp_publisher_relationships, but this is not a practical solution as even though after manual entry additional relationship entries show in the grid (and are acted on by EE) the additional entries disappear when entry is next saved. Plus working out the row-id and entry information to simulate the correct row in that table it is time-consuming.
Unclear what additional access / information you need to work on this - suggest you DM via Slack or some such to advise what you need.