Update your post to include full system hardware specs and OS information.
Include PSU: make, model, wattage, age, condition (original, new, refurbished, used)?
Disk drive(s): make, model, capacity, how full?
Make and model monitor? Connectivity (DVI, HDMI, DP)?
Try swapping in another known working video cable.
Does the monitor work without problems on another known working computer?
Does another known working monitor work on your computer without problems?
Determine if the problem follows the monitor or stays with the computer.
On the computer look in Reliability History and Event Viewer. Either one or both may be capturing some error code, warning, or informational event that occurred just before or at the time the monitor went into sleep mode.