arduino pro mini sleep / wake up with adxl345

The ten seconds are the inactivity timeout of the ADXL345 (you set it to 10s in the setup()). So you get interrupted from it after that amount of time. Deactivate that timeout and your Arduino will sleep forever.

Due to lines 140 to 144 I would have estimated to see at least the acceleration values for the first ten seconds. But - I don't. Can you also explain why?

I would expect it to see after 20s as you put the Arduino to sleep twice before that happens. Insert a Serial.flush() above each sleep command to have the serial queue emptied before it goes asleep.