Mac Pro Late 2013 keeps "shutting off"

When I say "shutting off", I'm not talking about "shutting down", it's as if it got unplugged or as if the power button was held down for 5 seconds. This has been happening quite a bit now, I'd be working away and then all of a sudden it shuts off on its own. And a lot of times it won't start back up unless the power cable is removed for 15 seconds and then reinserted. A few times it would begin starting up and then it would shut off.

There's nothing specific that I'm doing that seems to be causing this. I'm either browsing in Chrome or working in Photoshop or Illustrator. The only thing I do differently now before this started happening is that I started shutting the machine down when not in use, overnight or during the day while I'm at work. Then this started to happen.

Yosemite 10.10.3

Model Name: Mac Pro

Model Identifier: MacPro6,1

Processor Name: 6-Core Intel Xeon E5

Processor Speed: 3.5 GHz

Number of Processors: 1

Total Number of Cores: 6

L2 Cache (per Core): 256 KB

L3 Cache: 12 MB

Memory: 16 GB