I was able to quickly reproduce the problem you are seeing on my NUC system running Windows 8. After setting the alarm in BIOS, absolutely nothing happened when it reached the designated wake-up time. So, I did some Googling and found this: http://answers.microsoft.com/en-us/windows/forum/windows_8-hardware/bios-rtc-alarm-wakeup-fail-if-windows-8-enabled/88a7656d-2f21-4847-87a4-21e536a9b5e7
Are you running Windows 8?
The following site describes how to turn off Fast Startup: http://www.typicaltips.com/2013/02/disable-fast-startup-in-windows-8.html
After I did this on my lab system, the NUC woke up right on schedule.
Give this a try and see if it solves your wake-up problem.
Fast Boot in windows was the thing that caused the error
And it works the same way when using Windows 10.
Thank you for the information provided about this working with Windows 10* also.