Connect the external HDD to another PC and check what happens. If it plays hide and seek with another PC too, then the problem is in the HDD. If it performs reliably in the other PC then the problem is with the innards of your PC.
As simple as that. Is it not?
Your motherboard has a special power saving circuitry (Active Phase Switching) - an MSI innovation - that controls power to the PC, letting in more when needed and reducing it when not needed. I would naturally suspect a malfunction here, if it is not your main power supply. Just my thoughts.