Power button Solution
I just finshed repairing a Asus S550C laptop and yes the power loss fault was due to a power button issue.
The power button is located on a tiny circuit board (PCB) that is isolated from the main system board.
Asus uses a metal woven ribbon to ground the board to the chassis and the system board. Oh dear....
The problem is due to a floating ground caused by the ribbon cable loosing ground connection (floating ground).
If others are having similar issues (random power loss) as in this forum chances are it is due to this ribbon cable.
Disassemble the laptop and check to see if there is a ribbon connecting the power button PCB to the laptop chassis. If there is, clean the ribbon cable and power button. Lubricate the topside button (the user presses to power on the laptop) to make sure that it is not sticky. Make sure that the ribbon has good contact on the screw mounting hole and to the the chassis (there is a holding bracket on the bottom cover that holds the ribbon cable in place).
Re-install the bottom cover but before screwing it back down, power up the laptop to make sure it is working properly.
lacanausurfer :
Okay, my Eee is running fine again. I am sure in my case it was a contact problem in the power button. Cleaning and pressing it again and again while measuring the continuity went right.