"Permanent physician" is a concept that never existed before the ACA and doesn't exist now. 

There is no provision in the ACA that endorses or prohibits your insurer from keeping or severing ties with any particular doctor. That would be "socialized medicine."  The ACA -- as "conservatives" wrote it -- preserves market forces including your insurer's right to enter into (or not) service agreements with individual physicians - something they've done annually since Obama's kids were in diapers. 

Where do you think we live? Soviet Russia? Government doesn't assign you to a doctor -- or unassign you.