I had a somewhat similar issue with an Acer Aspire Aspire One ZG5 netbook, except my problem was that the device would power off after about 1.5 minutes from powering on.

Apparently a thermal cutoff switch needed some recalibration/replacement, so my fix was 2 hours in the freezer followed by a few more hours waiting for condensation to evaporate before attempting to power the netbook on again...

I used the above method for nearly a year before acquiring my present laptop, relegating the netbook to my growing pile of disfunctional hardware.