The issue is probably a bad battery calibration where your battery goes from either 100% or 50% to 0% after a full charge and green light.
You need to
1- charge to a green light,
2- reboot with charger in and charging.
3- Unplug
4- run the battery to auto shutdown

If you do this with the backlight forced to on and drain the battery with some big data transfer or GPS it only takes a few hours.
If the problem is not solved your phone rebooted before the battery could calibrate, it has sometimes taken me up to 3x tries but usually only one. I use the app batterygraph to track the voltage down into the 3.4v territory while wasting power, then I let up on the big data and let the backlight kill the battery for a few hours.
(edit)
I think the battery manager writes the final capacity at 3.2 volts right as it is also sending the shutdown signal.

I have since bought a new battery, then switched to SailfishOS on an Xperia XA2.
But thanks for your answers - my N900 still sits here, waiting for me to take the time to install Maemo Leste on it, and at some point this thread could become interesting again.