Can a lung puncture leak again after healing?

Yes. A collapsed lung (pneumothorax) is due to an air leak from the inside of the lung through the covering of the lung, out into the space between the lung and the ribs. The site of the leak has some damage, which will heal itself. The cause of the damage can recur, or the healing may not be strong enough, so a repeat leak can happen. It is not possible to predict if or when the lung will leak again.
Unlikely: new area. If a lung puncture truly heals, it is unlikely that it will ever leak again unless associated with other medical conditions such as emphysema or alpha-1-anti trypsin deficiency i which case the leak is more likely to occur in a new area.