Apple has already sold millions of iPhone 6s and iPhone 6s Plus handsets, and it seems that some are plagued by a bug that causes them to shut down unexpectedly.
The issue has been documented by new iPhone 6s and iPhone 6s Plus owners on Apple's support forum. The issue is simply that the handset randomly shuts down and will only restart when the power button is held down for a few seconds. It's annoying, and from the reports seems to occur a lot at night, which in turn results in people's alarms not going off in the morning.
Some owners claim that handsets that have shutdown also feel warm to the touch.
There have been some incantations that have been offered by others on the support forum to try to fix this issue -- mostly relating to a reset using Settings > General > Reset All Settings -- but none of these "fixes" seem to fully resolve the issue.
The latest iOS 9 beta builds don't seem to fix this issue, so a fix may be some time coming.