Sources suggest that it varies from person to person. Most professionals recommend wearing earrings for 2 to 6 months following the procedure. The ears will heal, but will not close up afterwards.
According to Bustle.com, cartilage piercings may close due to the lack of blood supply to cartilage. When jewelry is removed, the body may heal the hole with scar tissue, particularly if it was irritated from wearing cheaper jewelry.
Cartilage ear piercings usually take around three to 12 months to get completely healed. It is crucial for a person to routinely follow all the aftercare precautions so as to quicken the healing process as well as minimize chances of rejection.
Check out these cartilage piercing precautions from Bodypiercingmag.com.