Conclusions:
I thought it could be the ati driver
First I tried to change it with the vesa one and it suspended very

quickly; only X was not displayed correctly. So that I thought I could

give X a chance to run "on the fly" (without xorg.conf) and
1- the laptop is suspending/ resuming "the old thinkpad way" (i.e. in

a fraction of a second)

2- X is looking just as good as when using xorg.conf + vesa driver

3- "But" there is still a random power-off
After some minutes the laptop decides to power-off; as fast as if it

had been plugged without battery and you pulled out the power cable.
sigh...
Pau