But whether a few hours or a few days, eventually I start having issues with the displays. Monitors will black out. Not boot. Eventually the whole system just stops working in a way that I can figure out.
This sounds more like a hardware issue than software. Can you provide more detail? Have you done basic troubleshooting steps like trying different power cords and surge protector/power strip? What is the full list of hardware for your system? Have you reseated the RAM? Replaced the CMOS battery? (a dead CMOS battery will prevent system boot)