Need help with PSU/problem

http://pcpartpicker.com/p/ZNDZFT

PCPartPicker part list: http://pcpartpicker.com/p/ZNDZFT

CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor ($233.98 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($33.98 @ SuperBiiz)
Motherboard: ASRock Fatal1ty Z87 Killer ATX LGA1150 Motherboard ($111.62 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($84.29 @ Amazon)
Storage: Samsung 840 EVO 500GB 2.5" Solid State Drive ($259.19 @ Amazon)
Video Card: EVGA GeForce GTX 770 2GB Superclocked ACX Video Card ($301.98 @ Newegg)
Case: NZXT Phantom 410 (Black) ATX Mid Tower Case ($85.87 @ Amazon)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($71.30 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ OutletPC)
Monitor: Asus VS229H-P 21.5" Monitor ($139.00 @ Amazon)
Wireless Network Adapter: TP-Link TL-WDN4800 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter ($38.57 @ Amazon)
Keyboard: Corsair Vengeance K70 Wired Gaming Keyboard ($125.99 @ Amazon)

So this is my PC build and I got tons of feedback before I built it. It has been working fine for a month and I use it for many hours throughout the day. The past two weeks however it shuts off randomly. I figured it was either a graphics card, PSU or motherboard issue and only one stock fan in the front that came with the case would turn on, nothing else would turn on. No other fans, no lights in the case and no display or sound.

So I took it in for a second opinion and he found that one of the cords was loose either below the graphics card or near the cpu I forgot. He said they pop out slowly over time sometimes but if I have any more issues it could mean I need a bigger power supply. The feedback I got a month ago though everyone was telling me I could go even lower to 500 or 550 watt psu.

I played it safe since the 770 min requirement says 600w and got 620w bronze. So a week later with it working fine and now it's shutting off again, I checked the cords and it works again. Is there any way to keep the cords from getting loose? Or is it my psu not delivering enough power? Should I go up to 750w if I use my PC alot?

http://imgur.com/fyX8TnA

I took a screenshot of HWmonitor as well if this will help gather any more info, how much voltage or whatever is being used.

it isn't overclocked and I don't believe I'm doing anything at a heavy load. I played multiple games at max settings like Metro Last Light, Witcher 2, and Max Payne just fine without it shutting down. The only game I am playing right now is Dragon Age but it shuts off randomly even when I'm just browsing. And it can't be a heat issue since I'm always checking temps and they are fine. Highest I have seen is about 60-80. It usually stays between 30-50.

Everything seems to be in place as far as I can tell. And I had help building it, and just looked at the manual myself today when I was looking around inside. Also when I went to that other guy I asked him about the psu cables being hooked up right and he also said they were fine.

RMAing? Also how do you figure ram would be shutting down the PC? I will try it once I get home.

Okay well I tried the RAM method you suggested and it didn't work still so I guess that means send the psu back or get a new one. I'm sure I could get it working actualy again tomorrow cause it just likes to randomly work like that but I hate this random on and off crap.