Hi @dpstear ,
My answer will have assumptions as your description of the issue is not complete.
For you to auto-populate the supervisor in the column in SharePoint tells me that the item has been created. Is the item created via a Nintex form or another way?
When you open the Nintex form I am assuming it will be in edit mode and it is not picking up the user from the SharePoint column, ie the control is blank. As the control is blank, when you submit the form again after editing it, the column will be cleared as the control will be updating it to blank.
If the people picker control is clearing the column in SharePoint, this tells me that it is connected correctly.
Direction to resolve issue:
The path to the solution is to review how you are populating the SharePoint column. If the Nintex form is not picking up the value then there is an issue with the value.