Problem transferring large files

I had this problem with the last mobo I was using too. Here's what happens.
Let's say I'm backing up my sim (all 50 gigs of it
) and I start copying folders, one at a time to my back up drive, all seems well until I start to copy a really big folder (about 1gb or more) and the computer reboots.
I have the correct chipset drivers installed, the drives SMART status is normal and they test fine, and Memtest runs without errors.
I have found that I can copy the whole 50GB folder in one lump, if I do so in "safe mode", which made me think it was a driver issue, but again, I have double, double checked all of them and everything seems right.
Could it be a PSU issue, and why does the process work in safe mode?
Let's say I'm backing up my sim (all 50 gigs of it

I have the correct chipset drivers installed, the drives SMART status is normal and they test fine, and Memtest runs without errors.
I have found that I can copy the whole 50GB folder in one lump, if I do so in "safe mode", which made me think it was a driver issue, but again, I have double, double checked all of them and everything seems right.
Could it be a PSU issue, and why does the process work in safe mode?