Have you tried wiggling the AC power cord at both the wall socket (or surge protector bar)? You may possibly have a bad socket. Is anything else also plugged into the same surge protector preferably something that would stay off if its AC was interrupted. A light would not do since it could just barely flicker while that interruption would shut off the computer.
You may want to try it on a differnet AC power circuit. This would be a different breaker (or fuse) circuit from the one you are normally on. Is the AC outlet or circuit running on a ground fault interruptor protected circuit and if so, does the GFI trip? Coul;d it be reset by someone else if it is not right at your desk area?
Does this happen when you are using the computer or when it is just idling?
Is your preference setting to NOT start after a power interruption? You may want to, just for the heck of it, toggle this setting (In Energy Saver) on and off to see if it will result in a restart? If so, start looking more deeply at AC power problems.
Is there any particular program you are using when this happens?
Are you on some type of network where someone else could be getting control of your system? (Apple remote Desktop allows this kind of action.) If so, updates may have been remotely installed which will cause a restart or shut down if that is chossen by the remote administrator.
Has everything been fully updated? Some updates will shut the computer off for a restart. This is especially true for EFI type updates. This usually results in a restart which is not what you said was happening. Instead you got a shut down to a cold start. If that is the case then the updates are not the cause of your problem.
It is also possible that you could have a power supply failing. Are you still under three year AppleCare? If so give them a call to put the problem on record in case it develops to whare you need hardware repairs.