My daughter coughs at night. It never seems to go away. What could it be?

Could be asthma. Cough-variant asthma is quite common--basically just coughing and not much else. Post-nasal drip is also a common cause of night time cough in both children and adult. Reflux, which is more common laying down, thus can cause night time cough as some reflux of acid can get into the airway have your child see a doc...
Lots of Things. The answer to this question is highly dependent on several other variables - your daughter's age, current health problems, history, type of cough, etc. Anything from asthma to allergies can cause a chronic cough. Viruses, colds, infections can cause a new cough. Dry air can even cause a child to cough at night. Try a humidifier in her room if you live in a dry environment.
Many things. Night time coughs can be triggered by many different things. Causes include asthma, post nasal drip, heartburn(ge reflux) just to list a few. If this has been a persistent problem you should discuss with your pediatrician.
Nocturnal cough. A cough that worsens at night is often associated with asthma, infection (uri or pneumonia), gastroesophageal reflux, or rhinitis (allergic versus nonallergic). The cause is dependent on other details associated with the cough, and you should see your doctor to provide such details.