Seems that I am not the only one having that problem. Internet revealed, it's not the battery that's gone dead, it simply the netbook not recharging it. In some micro-code, there's is something preventing the accumulator, when deeply discharged, to be recharged.
Actually Acer is aware of this, and made a new BIOS available, solving the problem. It is said that since BIOS version 0.3309 the problem is solved. I flashed version 0.3310 today, and yes, the problem is solved. The accumulators are charged again!
Up to now, I only flashed the windows one and gave an initial charge to the batteries used with the linux machines.
Thus, if you encounter a similar problem with the AAO (110/150), this could be your solution.