Why would ones doctor keep their patient on lovenox (enoxaparin) beyond the 6 month mark?

Depends: On why you are getting lovenox (enoxaparin). If it's for deep vein thrombosis, and their are no other risks, it will often stop after 6 months. If it's for pulmonary embolism, anticoagulation should go for at least a year. If there is an underlying hypercoaguable state (cancer, enzyme deficiency, other chronic illnesses) it may be given indefinitely. In pregnancy, it would continue until after delivery.