While you have a decent rated PSU, it still a Rosewill, very generic and bland PSU. Further, you say you can't ID it, it suppose to have on the PSU "itself" some decal or sticker explaining all its specs, that better be there. It's important to find out if this is a single or split-rail design. As a split-rail design offers its amps across at least 2 rails of voltages(+amps) and connected too much on one rail and NOT balanced may tip the overload ckt.. Further, the Rosewill is on the cheap side, so it may not be actually offering all it can be and if it is, it is too easily over-drawn to safety factors. If this is a single rail design then that too still needs to spread the load abit if possible to help maintain a balance. Alas, the GPU maybe a tipping point too. If it draws too much when it use and becomes more demanding will also be a demanding item for the PSU. It alone wants at 150W for itself and increases for OC modes or higher video ram setups. Better PSU are 80+ rated and thier make-up is better build to include wiring and heatsinks and better components able to handle the stress. That's sustained output under load tells the better PSU out there. It will only get worse as time goes by. So, what people are telling you is correct and for this to happen so soon, I lean on the PSU being a weak factor. Better cooling is very important, so be sure IN at the frt, and OUT at the rear, that good airflow is present. Does it make any difference with the side cover off, does it remain running longer?
tada ------Willy 
I recently built a custom pc, and everything works fine except it shuts down by itself completely randomly, and occasionally does not turn back on right away. I have had it finished for about 2 days, and it has probably turned off by itself about 7 or 8 times. I have googled the issue and the most common answer is that it could be a heat issue or a power supply issue, the computer has not been put under any stress yet, and the power supply is more than enough to provide for the parts it contains. Any suggestions for how to fix it are appreciated.
Here are the specs:
Motherboard: Asus F1A75 M Pro
APU: AMD A8-3870K
GPU:Asus GTX 660
Case: Rosewill Challenger
Power Supply: generic Rosewill 700w (can't find the model anywhere its not on the box or anything)
RAM: G.SKILL Ripjaws X Series 16GB
Hard Drive: generic Western Digital 500gb
OS: Windows 7 Ultimate
CPU generally runs at about 32 to 36 degrees celsius and mb generally runs at about 30 to 34 degrees celsius
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