After about 6 hours of trial-and-error, uninstalling programs and motherboard drivers, I determined the culprit was the EVGA USB 3.0 Intel eXtensible Host Controller driver.
The computer would sleep and resume just fine multiple times after uninstalling that driver.
Then I found this FAQ from EVGA, followed it precisely regarding in what order to install drivers, and then to reboot and disable Windows 7 Boot Option in BIOS, and it seems to be working ok now with the USB drivers installed.
http://www.evga.com/support/faq/afmviewfaq.aspx?faqid=59652
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12. Download the most CURRENT DRIVERS from EVGA in a primary directly called Z170 Motherboard Drivers, which are:
a. .NET Driver, Version 45 or higher
b. Audio Driver, Version 431 or higher
c. Chipset Driver, Version 10.1.1.7 or higher
d. Chipset Network Driver, Version 30.100.1519.08 or higher
e. Intel HD Graphics (optional)
f. Intel ME (optional)
g. USB 3.0 Driver, Version 4.0.0.36, or higher
13. Upon all MOST CURRENT drivers downloaded from EVGA,
follow the order of loading of the updated drivers:
a. Chipset Driver
b. Chipset Network Driver (you will see at the end of the update, a reference to the I/O being updated.
c. .NET Driver
d. Audio Driver
14. The LAST UPDATE should be the USB 3.0 Driver, most current version.
When this update is performed, you WILL LOSE all USB conductivity for approximately 40 seconds to about a minute;
however the keyboard, mouse and all other USB ports will be fully operation after that.
15. If the system wants to restart after this, BE SURE TO ENTER THE BIOS upon the RESTART, enter through the BOOT tab
and DISABLE the Windows 7 Installation. Save and exit.
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