I've been having the problem with my G75VW for the past eight months, and have gotten to the point where I've just decided to live with it and use it primarily as a multimedia laptop. I had the GPU replaced under extended warranty, replaced motherboard, tried a different SSD and different HD, clean-installed Win7 64-bit and Win8.1, replaced RAM, repasted CPU and GPU, etc. It still reboots at random times - sometimes under heavy load on the GPU and sometimes almost immediately after login to Windows. CPU and GPU temps run on average around 50C. Not a speck of dust inside (I've had the thing broken down to bare parts more times than I care to think about.
ASUS support took over a month to turn around the RMA work on the GPU replacement, and it didn't resolve the problem. I bought and installed the motherboard on my own. Still shuts down. What I'm thinking now is an inherent defect in the mo-bo design, or a defect in the power adapter or shorted power jack that clips on to the mo-bo.
It's a shame - it's a great laptop still and has all the features I would want in a gaming system, but it just won't stay powered on for a predictible length of time. I'm not relegating it to the trash bin, but it has been demoted from a powerhouse gaming rig to a glorified video player.