Remember to switch into the AutoTune flight mode (accessible either using a flight mode switch or the auxiliary switch) from AltHold or Loiter.
Also the most common problem that exhibits the symptoms you're seeing is that the sticks are not perfectly centered. In this case it thinks the pilot is trying to override the position and so it won't start twitching. This can normally be resolved by re-doing the transmitter radio calibration. http://ardupilot.org/copter/docs/common-radio-control-calibration.html. Another alternative is to increase the size of the RC deadzone (i.e. increase RC1_DZ, RC2_DZ, RC3_DZ, RC4_DZ to 50)
I'll be updating the autotune wiki page in the near future and I'll add a "common problems" section that includes this additional advice. AC3.6 will include better feedback to the pilot on the state of the autotune.