Have you upgraded to the latest BIOS? Do you have all of the Windows 7 updates (all 245+ of them - and almost 1GB of downloads ) installed? Do you have all of the latest drivers installed?
Thank you for joining the Intel communities.
Have you checked if maybe a program is not closing correctly and it prevents it to shut down, do you get a message when trying to shut down the system?
Check your Windows task manager to see what programs are running before shut down the system and close them, then shutdown the system and see how it goes or check what programs are running on startup, maybe that is causing the issue.
Check the device manage to see if all drivers are correctly installed, sometimes corrupt or damaged drivers can cause the computer to lockup when shutting down.
I suggest trying N. Scott Pearson recommendations, run Windows updates to install all possible updates and update the BIOS.
You can download the latest BIOS version for your system here:
Please see F7 BIOS Update Instructions for Intel® NUC