This motherboard was a GA-MA790FX-DQ6, but the option I describe below is present on my other Gigabyte products. That is why I decided to share this information with the forum.

I upgraded the BIOS to F7G. I installed a new CPU and my system would not enter standby any longer. When I wanted to wake my system up, it restarted the hardware as though I had powered down.

Originally the system had an AMD 2+ CPU. I upgraded the processor to AMD 3, and that's when the problem started. However, my other similar system (AMD 3 CPU/AMD 3+ MB) worked flawlessly, so I knew it had to be something with the new BIOS that supports AMD 3 processors, and not the processor.

When in BIOS, CTRL+F1 > MB Intelligent Tweaker (M.I.T.) > DRAM Configuration > CKE Power Down Mode: ENABLED

The rest of my DRAM settings were all AUTO.