How predictably is this happening? I know you say it has happened few times a week but if you cycle the device between sleep and wake several times will it happen or only after it's been sleep for awhile or it doesn't matter if it was just on and you wake it again it might happen and you just never know?
Ask because one way to rule out this being caused by an app would be to run the device in Safe Mode but if it takes days to happen... No one wants to be in SM for days.
Is there anything you can say about this. Any pattern you've noticed? It only happens in the morning when you first check the device. It seems to happen more if I played this game or used this app before putting the device on the charger. It happens more if I have the device charging than when I'm out running on battery all day.
If it is that unpredictable I would try this, try closing all of your background apps before putting the device to sleep. Bring up the multi-task screen and close all open apps for two days or so and see if it happens. It's a lot of work and remembering but if it is being caused by an app this might help narrow it down.
From your description you are putting the device to sleep then waking it. So you're pressing the power button twice when this happens? Once to seemingly put the device to sleep and once to wake it again? If it goes dark and you attempt to make a selection on the screen can you open an app? This leans more towards a hardware issue. I might put an app on the home screen, something like a game or a messaging app, in a spot I know I can find even with the screen dim. When you attempt to wake the device and it does this try to open that app. Then check to see if the screen comes on when the app is opened and/or see if the app is open when you wake the screen again and it's working. I'm not sure what to think if the screen lights if the app is opened... That will take some more thinking. However if the app is open when you unlock the second time that would begin to sound like a back light issue. From there I'd try to figure out if the screen is displaying anything, which without a backlight can be difficult. You might be able to shine a light on the screen from an angle or something to see if your icons are present. You could also try covering the light sensor at the top of the phone, holding it briefly, then releasing it. If you're using adaptive brightness, the screen normally dims in dark places to reduce eye strain and brightens in light places to make the screen glare resistant. In essence you would be nearly turning the backlight off and then on again.
Let us know what you find.