Getting too little sleep is bad for your health. But getting too much—as wonderful as it may sound to some—can be problematic too.

The powerful need to nap during the day can be a warning sign of many health issues, from diabetes to depression, low thyroid or obstructive sleep apnea. When doctors rule out such explanations, it is called "primary hypersomnia," an umbrella term for several conditions that make sufferers crave sleep, despite getting 70 hours or more per week. One of the best known is narcolepsy, a neurological...