It's possible to have recurrent pneumonia when their are risk factors. Getting rid of such risk factors will be helpful.
Some children have issues clearing secretions from their lungs e.g cystic fibrosis. These children are prone to recurrent infection.
A foreign body in the airway will also cause recurrent infections.
So if a child is having recurrent pneumonia, see a paediatrician for evaluation.
Once pneumonia is treated appropriately, it has cleared! If your has a chronic cough that is not resolving with treatment he/she needs to be evaluated for causes of chronic cough.