Ok i'll be brief...
use a late 2011 13" MBP connected to the display in question; OSX is Yosemite (was using Mavericks originally when got the Monitor and the problem); have had numerous Apple calls and still have an ongoing chat with them.
Apple walked me through many different configurations plus SMC & PRAM resets AND numerous restarts.
All efforts to wake monitor failed whether manually put to sleep or computer put itself to sleep.
As of today this is what i can report with my specific situation:
at any one time I have a minimum of six apps open
My default browser is chrome (no commentary please)
Have a USB Apple Keyboard, USB & 800 FW EXTernal Drives all attached to Monitor
Settings: Monitors selection is on mirror mode. Put Hard Disk to Sleep is unselected.
I restart my computer depending on the situation once in 1 -3 weeks. It only is put to sleep; unusual to turn it off.
During the last Failed wakeup, (Apple technician and i hadn't spoke for 5 days), on the call yesterday she suggested I restart the machine without any of the peripherals attached to the back of the monitor. We then plug-and-played and with each new configuration put Computer to sleep for a couple of minutes and upon pressing the external keyboard the monitor would awaken (With the computer). Yay!
At that point we decided the only two elements left that could not be checked simply, (I would get in touch with her today after my findings) were third party apps (Duh) and Time!
So whether manually applied or letting the machine go to sleep by itself Monitor turned on every single time at 30min, 70min, and at 105min.
Now, this is where I had an "Ah Ha" moment as I realized two applications I had not reopened purposefully (as they take awhile to reload) when the computer was restarted originally yesterday: Direct Mail and Chrome.
I added them both back did some work then put the machine asleep. 4hours later came to see if it would awaken and NO!
I immediately realized since Chrome is my browser of choice it is ALWAYS open before the computer goes asleep in any of these scenarios!
I quit Chrome put the computer to sleep and 10min later I decided to check and indeed it awoke; no restart. Wow!!
I left all the apps I use opening running except Chrome and let the computer go to sleep; keystroked the USB keyboard this AM after 6hours and Monitor awoke.
I did more tests myself and have come to the conclusion:
if allow computer to go to sleep or manually put to sleep with Chrome running with other apps the monitor never awakens when pulling computer from sleep; Any other time the computer always awakens the monitor as long as Chrome isn't running.
My solution: quit Chrome when leaving computer for longer than 15min as that's when it puts itself to sleep.
I understand many of you have found a solution using the terminal command; that's great. I prefer not to do that as I was clear my situation was third-party related since all configurations testing and time testing worked out.
If I find that longer time (Beyond six hours and Chrome closed) and the machine does not awaken the monitor, I will report back.
Thought I would share my findings here and maybe it could be a solution for one of you. Thanks! Peace