mosfet is connected source to external 3.3V and drain to the board: as to be able to cut the power using gate signal (pulling gate high).
Based on your "hint" I powered up the board from laboratory power supply and set voltage 3.6V. Onion now works as expected. So definitely voltage drop across mosfet is more than 0.3V and that way, Onion Vdd get down to minimum allowed 2.97V causing an reset (and reboot: because voltage "recovers" to acceptable level).
Thanks for your help.