Causes of chronic cough can include:

• Asthma - People with asthma have inflamed or swollen airways, this may cause wheezing and shortness of breath. Sometimes the only symptom is a cough that is made worse by viral infections, is worse while you are asleep, or may be triggered by exercise and/or cold air
• Nasal and Sinus Disease - Postnasal drip or a sinus infection (sinusitis) can produce chronic cough. Usually other symptoms are present, but sometimes cough is the only symptom.
• Stomach/Esophagus - Sometimes, stomach fluid moving back up the throat. This is called "reflux" and may occur silently without heartburn (like acid taste in mouth, chest pain). Some people may develop a hoarse voice and/or choking as symptoms.
• Post-Viral Cough - After having a viral respiratory infection,  a cough can last for weeks to even months. There is no specific therapy for this cough, it eventually goes away. 
• Inhaled Foreign Body - Foreign bodies, such as toys and food, can be accidentally inhaled at any age, but most commonly occurs at ages two to four years. It can cause a cough to continue for many weeks to months.
• Habit Cough - This is a persistent cough of childhood that has no clear physical cause. It occasionally persists after a simple viral respiratory infection. The cough is typically dry and repetitive or is a "honking" cough. Habit cough usually occurs only when your child is awake, not sleeping. A neuromuscular tic can also cause this kind of cough.
• Irritant Cough - Exposure to tobacco smoke and other pollutants (smoke and exhaust from wood burning, air pollution,  exhaust from vehicles) can lead to cough and may worsen the cough associated with asthma or rhinitis.