laptop - Batteries react strangely

A school has several identical laptops bought 5 years ago: Fujistu Lifebook model A530

Since several weeks ago, around 50% of them randomly turn off after 1 to 5 minutes:

• The shutdown is sudden: one second you work on the laptop, the next second it is completely powered off


• Swapping the batteries of a working laptop and a broken laptop causes the working one to fail, and the failing one to work. So the problem follow the batteries


• Only when on battery. Plugging the power cord in fixes the problem. Once unplugged, the laptop will shut down after 1 to 5 minutes again


• Idle CPU, low memory usage. Happens even when no one is using the laptop


• The battery charge state doesn't change anything


• After a sudden shutdown, we can reboot the laptop without problem because the battery is still charged as before. But it will stop 1 to 5 minutes later


• Only happens while in BIOS or running Windows 7 pro 64-bit. Everything is fine while running Linux booted from a USB key: it runs 1 hour without problem


• The laptops worked several years without problem, and nothing as been done recently (and more: they are theoretically identical from a software point of view, so why only 50% of them?)


• I don't see any strange programs or anything

Answer

I flashed the BIOS et voilà, evrything is back to expected behaviour.
So I flashed each laptops. They can now use the laptops during more than 40 minutes (which is good for 5 years old batteries).
With Linux this changed nothing, so probably relying on a driver resetting the battery controler after boot.