This is an issue that has been on and off for some time now. I'll put my computer in S3 hibernate mode and when I go to resume the computer will turn on but the video will not turn on. the only way to get it back is to restart. Then, a couple weeks later, it will start coming on again. And begins the viscous cycle.
I have updated video drivers
everything is enabled to wake up S3(using wireless keyboard, usb mouse).
msi AMD 790x
You can always set it so that your computer doesn't hibernate, but I don't know if that's something you want or not. I'm guessing the system probably seems to run fine otherwise. Regardless, the PSU is probably on its way out, and I would recommend replacing it sooner rather than later since it is an Ultra PSU, a brand I don't consider to be reliable.
Edit: I have heard of cases where certain motherboards have problems coming out of hibernate mode. I'm not sure if that factor is in play here, but maybe someone else can come along and provide some insight into that.
I just fixed that problem on my system, after years of accepting it. My Asus motherboard power settings had something like "Re-post video on wake from S3". Turned it off, and the system wakes up just fine. I guess Re-post didn't mean put it up again, but run the Power-On Self Test.
If you are running Win7, look up the difference between Sleep and Hybrid Sleep and set accordingly. My PC was defaulting to Hybrid Sleep, which writes a hiberfile just in case. So after waking up with no video, I would reboot and the darn thing would resume from hibernation - although I had not hibernated!