I'm guessing that in each loop, she died directly or indirectly because of the prince. As a merchant, she died because she got dragged into the war caused by the prince. As a herbalist, she died after contracting a disease in a plague ridden place, which I think is a product of the war. As a knight, she died at the hands of the prince/emperor. Not sure about the other lives, though. Theory: To stop the loop, avoid the war.