Hi,
 
Unfortunately, as you mentioned the motherboard is well outside of the warranty period and we do not offer an out of warranty service option.
 
I can suggest to double check that the battery holder does not have any corrosion on it and if it does you could try to gently clean it. 
You may also double check the button battery that you installed to ensure it was working properly. 
 
Beyond the above suggestions you could keep the system plugged in to avoid power loss as it should not lose the time and date settings when power is not dropped to the system.

is anything touching / possibly shorting the "Clear CMOS Jumper Posts"  - front or back of MB
 
https://www.evga.com/support/manuals/files/111-CS-E371.pdf   (page 10 & 14)
 
12. Clear CMOS Jumper Posts
The motherboard uses CMOS RAM to store set parameters. Clear CMOS by
bridging the two posts with a jumper or metallic object, such as a screwdriver.
This feature has two main uses: The first is to clear BIOS and power on before
updating the BIOS, and the second is to troubleshoot when the motherboard
fails to POST (e.g. after upgrading RAM or CPU, adding new hardware, a failed
overclock, etc.). These posts provide a much faster means of resetting CMOS
than removing the CMOS battery and discharging power to the board.
 
If that is not the issue ....
 
- Disconnect everything from case & unneeded USB ... to test if case devices or USB have a short
- try removing then cleaning & inspecting the MB
 
"tin whiskers"  could be the cause
 
 
MITIGATING AND PREVENTING THE GROWTH OF TIN AND OTHER METAL WHISKERS ON CRITICAL HARDWARE