Default configuration for the interrupt pins is active high, so why are you activating the interrupt at low?
If the above description of the connections is the complete wiring (you should post a wiring diagram) you probably have the problem that as soon as the Mini falls asleep, the pull-ups for the I2C get inactive and the bus is floating. In that state the reaction of the ADXL345 is not defined, so you don't know what will happen.
Most probably you have another wiring, as with just the internal pull-ups you may damage the ADXL345. I guess that you're using some kind of breakout board but you didn't post the schematics of that board. This information is important.