After installing Linux Mint 12 on the EEEPC and fixing some immediate post installation issues my netbook has been working fine in all but one last thing. When running on battery power the EEEPC often warned the battery being near to full discharge. Sometimes the computer went in automatic power off even with the battery almost fully charged.
It's no new that the early EEEPCs battery aren't properly recognized on most of Linux distributions. That's because of the buggy way EEEPC BIOS handles ACPI, I noticed it since I first installed Ubuntu years ago, but it usually never been a problem apart from some meaningless estimation of the battery duration.
After some research on the Internet I came at discovering the cause of problem, and the solution, mainly thanks this AskUbuntu page. The problem is due to a new Gnome default settings in power management, these settings make the system use the estimated battery time (instead of battery charge level) to decide whether to warn the user or even to shut down the computer. A good thing where the battery is properly handled but a disaster for those laptops (not only EEEPC) where it isn't. By the way the solution is restore the old settings.
I so installed the gnome configuration tool dconf-editor using apt-get command:
sudo apt-get install dconf-tools
eventually I set to false the setting placed in the path org.gnome.settings-daemon.plugins.power.