At first I thought that maybe a setting in the BIOS (Wake on LAN - invite WOL, USB devices, ...) could be responsible. These functions are all but shut down. Even the existing Windows is always "shut down", the "Power Save" is never used.
After my current Kenntnistand the batteries either a problem with self-discharge or the notebook-circuits have to pull the on / off switch within 14 days the amount of electricity that the battery is completely discharged. The battery has no capacity problem! When the battery is fully charged, you can take the notebook loose 2.5 hours working without power supply (230 V) to have to suffer.
If the topic I learn anything useful from the manufacturer, I share this with here.
Update (February 2014):
The Fujitsu-Support recommended in my case a BIOS update from Version 1.12 to Version 1.16. But satisfactory results I could achieve only after I under the BIOS settings the function: have switched off "Anytime USB Charge" ("Disable"). For this function, there is in the BIOS settings: "Disable", "AC" and "AC / Battery". For me would be "AC" desirable because then one on USB connected device could invite as long as just the notebook power adapter is plugged in. The "AC" setting, the problem was not resolved with me!
Remain with the setting "Disable" after charging to 100% after 13 days without turning and without power supply connection yet 75% charge in the battery. From my perspective, that's ok. It should be noted that the charge status display under Windows 7 can also be seen rather as an estimated iron, ie, it is not particularly accurate.
One commenter suggested here earlier to set up the program "Fujitsu Anytime USB Charge Utility" accordingly. On my notebook ("Windows 7 prof 64 bit German") is not working at this downloadable Fujutsu Program. Report The German and the English version at startup errors and quit on their own.
Conclusion: The AH502 and his relatives (.. For Ex AH512) are useful, convenient device. Also the Fujitsu support has made a good impression on me. I raise my rating is now just two to three stars. The battery problem, however, has cost me a lot of time! Without the battery concerns five star would be conceivable.