- 'Doesn't jump', I mean ATmega doesn't react on it.
That's strange because that denies my theory below.
- I'm using internal pull-ups. Could this be the problem?
That could be a problem.
Using the internal pullups, the I2C bus will go in a floating state when the ATmega goes asleep. It may set the ADXL into any state, that's why I assumed that the INT1 will never be activated in this case (see above). I would install external 4k7 pullups and try again. As long as there's no activity on the bus this shouldn't consume much power.