From what you have described i would be looking at the auto switch feature between analogue and digital signals. The first thing to do would be to borrow a monitor from someone and plug that onto your pc and see what happens. I personally have never found a problem like this relate back to a motherboard fault, you would be experiencing other problems with your pc if either the northbridge or southbridge had become faul;ty, and tbh, your pc would be bloody unstable if this was the case.
So no.1 - Try a diff monitor crt, tft dfont matter as long as its working order.
If you tried a crt, put your current monitor back on and connect using a vga cable and see what happens, If problem persists your monitor is faulty.
If you tried a tft with digi connection, reconnect curent monitor with digi cable and see what happens. Again if problem persists your monitor is faulty.
No.2 - If you find the test monitor to suffer the same problems, try a new cable.
I stuggle to believe that the problem is relating back to the pc, given that the pc isnt turning off, or freezing up or anything other than running stable.
Let me know and we can work from there.
Ash