It all depends on the power level they're driven at. If they heat up to more than 60-90C or so on the die, they start burning out.

As a real world example, the maglite led bulb has extra circuitry to automatically reduce power when it gets overheated. This happens after about 2 minutes, after which brightness starts to drop. Usually not noticed by the users, as humans are terirble at perceiving relative brightness.