New build shuts down randomly - insufficient power?

I have an ongoing problem with my new build shutting down randomly. It is very sporadic: it can be 5 times a day, or once in 5 days.

My temperatures are fine, I have tested the wall sockets and have the latest (Asus BIOS). After shutting down, the reboot/shutdown cycle loops until I manually power off. On reboot, there is no anti-surge waing.

Recently, I unplugged 2 120mm fans, 2 sticks of RAM and an SSD. It has not happened since. I am wondering if my power supply is insufficient (although it is an AX860i from Corsair). Is that possible, particularly if the Titan is drawing a lot of power?!

Spec: 
Intel i7 5820
EVGA Titan X Hybrid
8 x 8GB DDR4 RAM (Corsair Vengeance)
6 x 120mm fans 
Noctua D15 cooler
4 x Samsung EVO SSDs
Corsair AX860i PSU
Sabretooth X99 mobo