Video card works... sometimes

I put this build together on Wednesday, and have run into a problem: my video card doesn't always work. Apologies for the wall of text, but I wanted to describe the problem and symptoms in detail because its just so weird.

When I bread-boarded the system before putting it in the case, the video card worked fine. It also worked fine the first night I used the computer. When I powered up the next day, the system turned on, but showed simply a black screen. With speakers plugged in, I could even hear Windows load.

So Thursday night, I opened the case back up, double checked all my connections, and re-seated the video card. That didn't work, so I changed the display to use the on-board graphics, which were working fine. In the BIOS, it showed that the card wasn't even recognized as being in the PCI slot. I tried re-seating multiple times (5 or 6 times, probably) until the card started working again.

Friday night, I come home, power up, and see a black screen again, with the Windows start-up sound playing in the background. I try powering down and back up again multiple times. Switching to on-board video works fine. I check the BIOS, and we're back to no card in the PCI slot. So I leave the display hooked up to the onboard graphics and use the computer for 10–15 minutes. Then I shut down, switch over to the graphics card, and everything works like it should. I think it's probably important to note that I never took the case off/unplugged/re-seated anything. Same deal Saturday and Sunday.

Once the system successfully boots with the graphics card, it doesn't seem to stop working, until I try to use it the next day. I've been able to use it for hours at a time without problem, once it successfully boots.

So... who's got ideas as to what's wrong? My current theory is that there's a bad connection/solder point that doesn't like the cold. (It gets down to ~20-30 Fahrenheit during the day in the house.) Thanks for any help you've got!

Here's the build:

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard
Memory: Crucial 8GB (2 x 4GB) DDR3-1333 Memory
Storage: Seagate Barracuda 2TB 3.5" 7200RPM Internal Hard Drive
Video Card: HIS Radeon HD 7850 2GB Video Card
Case: Antec Three Hundred Illusion ATX Mid Tower Case
Power Supply: Corsair Builder 500W 80 PLUS Bronze Certified ATX12V