My Macbook Air Shuts Down after receiving no input/activity for 5-7seconds

This constantly happens - if I go 5-7 seconds without any keyboard or trackpad input into the mac, the "Would you like to shut down your computer" dialogue box pops up, stays up for a couple of seconds and then the computer powers down. This happens regardless of whether the computer is performing any tasks - such as music or video playback or background downloading, etc. It also happens if I boot into Safe Mode. Occurs regardless of running off the battery or the power supply.

Having a stationary finger permanently on the trackpad or keeping a key pressed on the keyboard is enough to prevent the issue from manifesting. However, this is less than ideal for obvious reasons of preventing any mobility as one hand must be constantly on the computer when I am using it.

Having a finger on the trackpad is not necessary during the start up procedure, which typically lasts about 20seconds - yet the computer does not shut down during this despite having no input. This makes me think its a software problem rather than a faulty power key - If the wiring on the key was malfunctioning and therefore registering as if the power key was being pressed down, wouldn't that result in a shut down midway through startup?

Things I've done to try and fix this that have all failed:

- Downloaded the SMC Firmware update

- Reset SMC a number of times, as the first time I did this, the problem fixed itself/went away for about a week before manifesting itself again. Future resets have been unsuccessful

- Reset P-RAM

- Let the battery drain out completely

- Upgrade OS to Mountain Lion

Information about the computer:

- 2011 13' Macbook Air

- The exhaust fans work

- Was running Lion, currently on Mountain Lion (10.8.4)

- All software updates, firmware etc is up to date

- The power key does work, i.e it does shut down or start up the computer upon being pressed

- No liquid spillage has ever occured

- I don't think it is related to overheating as it happens within seconds of being logged in when no intensive tasks are occuring and when hte laptop exterior feels quite cool to touch. Also, the exhausts work as normal.

- There is no pirated software on the computer, if that makes a difference?

Any help on how to fix the issue or at least manage it better would be greatly helpful! Let me know if you need any more details or a video recording of what it does. A Genius Bar employee merely suggested replacing the keyboard for AU$200 without even opening it up to check if there was an issue with the keyboard/wiring and spent maybe 10seconds with it.