Hi there,
I'm not sure why you are having these issues but I have come across similar issues before. The thing to do is to try and find out the root cause of the problem and that is always easier said than done.
In an effort to troubleshoot, have you tried running your RAM at 1333MHz rather than its rated 1600MHz? Sometimes this can help and it is worth trying if only to eliminate this as part of the problem.
Looking at the User's Manual for this motherboard, Gigabyte recommend a PSU of at least 500 Watts:
To meet expansion requirements, it is recommended that a power supply that can withstand high power consumption be used (500W or greater). If a power supply is used that does not provide the required power, the result can lead to an unstable or unbootable system.
If you have access to a different PSU it would be a could idea to try that as this can be a major cause of BOOT/Reboot problems as the power draw is usually at its greatest during this process.
If you are using external USB Devices (apart from mouse/keyboard) try powering them down or removing them to see if they are causing the problem.
Check Power Saving Options in Windows and/or any Power Saving Software installed, to see if it is responsible for the monitor shutting down.