It seems to be a hardware stability problem. Is the cpu overclocked? Have you updated to the latest bios? Maybe the power supply is having issues under high load? Hard to say.
Turns out it was the power supply! I wasn't overclocking and I don't think it had to deal with a high load. I hooked up a kill-a-watt to the machine and the max I saw it pulling was 85 watts and the supply is rated for 450 watts. I ended up buying a higher end power supply and the problem went away. It's strange that the hanging happened with a specific set of criteria. I would think a power supply issue would be random.
Either way, I hope this thread helps people out of they see the same thing in the future.
Thanks for your help!