Most people don’t cough much while they’re asleep, especially during REM sleep. Sleep shuts down your cough reflex. If you do cough while asleep, chances are you’re not getting good rest. It may also be a sign of a sleep disorder. A chronic cough is a symptom of obstructive sleep apnea. That’s when your throat muscles relax and block your airway for brief periods of time. If you think you have this, see your doctor.