Sounds like a bad battery. Do you have a spare, or a friend with the same model you can switch batteries with to test this out?
There's also this thread about the Acer Aspire One battery that a BIOS update seems to fix.
http://www.flyertalk.com/forum/trave...ne-6-cell.html
Have you checked the Acer web site to see if there's an updated BIOS for your model?