Hello,
The next time this occurs do not power off the PSU.
So lets say you turn on, the green light flickers.
Leave it like that, unplug the 24pin ATX and 8pin EPS connector from the motherboard.
Short the green and black wire on the PSU to see if it powers on the PSU / hard drives.
https://www.youtube.com/watch?v=5FWXgQSokF4http://www.smps.us/atx-connector-20-24pin.jpegThe reason for doing this as is occurs and not powering off the PSU is to see if a protection circuit was tripped within the PSU. If tripped, when you try to short the psu it will not turn on. Disconnecting the power from the PSU will reset this circuit so you must leave it connected when the issue occurs.
This tells you that there is a physical fault.
If powers on, the motherboard is causing your issue.
Whilst looking, check all the pins in the ATX/EPS connectors / board and PSU to see if there is any signs of burning.