Please keep in mind that your Intel® Compute Stick Supported Operating System is Windows® 10, Kodi® has not been validated by Intel®; If you are running Kodi® for Windows® bear in mind that it says that, runs natively on Windows Vista, Windows 7, and Windows 8.
This is some information I could find about Kodi® for Windows® I hope this could help.
In this link is the Supported Operating System for Intel® Compute Stick
Check this link to get more info about Kodi® for Windows®
Kodi® Frequently Asked Questions about Windows® and Windows®-compatible
Kodi® Power settings
I have Kodi for Windows. (Maybe like 90% of ICS users)
There is no reason for this - after correct shut down and turn extension cord switch to off and on, ICS is still off. Kodi is just normal software what say to Windows to turn off.
If i just switch extension cord switch to off and on, without correct shut down the windows, everything is ok.
Please let me know if what you want to is to have the compute stick on after power failure, because after a normal shut down on Windows®, your Intel® Compute Stick STK1AW32SC will need you to press the power bottom to turn on again.
The wake after power failure option in the BIOS is not available on this Intel® Compute Stick STK1AW32SC; this option might be available on Core™ M sticks in the future.
STK1AW32SC has power settings - Always ON
Problem solved with an extension cord with switch: When I turn off the normal shutdown even switch on a power strip and when you turn it on again (for at least 30 seconds) turns on itself.