Computer dies on me (can't say it better due to no technical knowledge; pls read :-)
The 'click' sound you hear when your computer goes off is the hard drive head parking itself. It does this whenever the machine shuts down to prevent damage.
As for the problem itself, I believe your computer is overheating. There are thermal sensors in your computer which automatically kill the power before temperatures get high enough to cause damage to the components inside. This also may explain why ACER Labs weren't able to find a problem: they most likely have their lab air conditioned and set to a relatively low temperature. I suspect that you tend to use your computer on your lap or on a desk surrounded by a lot of clutter. This reduces the available airflow, and may cause the cooling system to re-use warm air instead of fresh, cool air to ventilate your computer. One possible reason it may have gotten worse lately is an excess of dust, lint, cat hair, smoke residue (if you smoke), etc., has clogged the heatsinks that channel the air, reducing the airflow, and literally insulating the components,
There are a number of products available to help you with this problem, however our first task is going to be to remove any build-up of foreign matter on your machine. Most office supply stores sell cans of compressed gas. I would recommend purchasing one and applying it liberally to the vents on your computer. Make sure that the machine is turned off (and unplugged, with batt. removed, for extra peace of mind) and spray the air into each vent opening, being careful not to invert the can (the compressed liquid may come out, which may cause condensation, leading to a short circuit if the battery / power is reapplied immediately). Once you have done this to each of the vents twice, let the machine sit for about 2-3 minutes before reinserting the battery / power cord. This should take care of the immediate problem, however you may still have issues with the device overheating depending on the environment you use it in. To combat this, I recommend purchasing a 'laptop pad'. They can also be found in most office supply stores, and provide either a raised surface for the laptop, to allow more airflow, or on some of the more expensive models there is a fan to actively generate airflow.
To prevent this from happening again, I recommend dusting your computer's interior about once a month.