How do I stop connection loss from monitor?

I have had my Asus for only about a year now, it has been running great for the longest time but now im having problems with my monitor losing connection, while im gaming, and if im away from the computer for too long. i have brought it to best buy for tech support 3 times already but they havent helped. they suggested restoring my entire system to factory default.

someone please help
additional info, no upgrades have been made to this computer, no new parts, only the monitor goes out, the tower is still active
 
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