I was dealing with this issue since I built my PC in 2010. I thought it was CPU and GPU overclocking related so I simply disabled the sleep and standby functions. However, these sleep and wake up issues persisted long after I reverted back to stock speeds. I left it for a couple of years and this past weekend, I decided to perform a quick Google search and found the solution.
Computer with Gigabyte GA-H55M-USB3 motherboard does not wake from sleep or the monitor remains dark after the computer wakes up.
Disable the integrated serial port in the BIOS.
Go to Integrated Peripherals -> Onboard Serial Port 1 -> Change value to [Disabled]
Hopefully you don’t need your serial port (most people don’t). I haven’t experienced any wake up issues after disabling the serial port, I will update this post if anything changes.