Press ON - Hold OFF latching circuits
Try connecting a load because the leakage current from the p channel mosfet will turn on the n channel mosfet which in turn will activate the p channel mosfet and reproduce the unwanted effect you witness. It needs a load and not an open circuit. Take note what it said in the original circuit description: -


  For it to reliably turn OFF, the load should draw sufficient current
  so that any downstream capacitors will discharge within a few seconds,
  allowing the gate drive of the N-MOSFET to decay.