Could you post some pics of the internals - particularly the pstat and pstat wiring. This is stumping me - at first I want to say the pstat operation is at fault because drawing off hot water will cause the pstat to operate just as will operation of the steam wand. But the pstat is in operation during the machine warm-up and idling phase also.

The pstat is a machine's "thermostat" as boiler pressure and temperature are inextricably linked. Does the machine reset itself or do you have to turn it off/on?

Note that 1st-Line is a Bezzera dealer and might have some better answers - http://www.1st-line.com/

Before you do this (and sure, it may solve the problem) why not open up the control box and look for obvious signs of distress?

In addition, I previously said that BOTH wires from the level probes must go directly to the control box. Is this so? Disconnect the wire leading to the long probe (at the probe) and temporarily ground it at a KNOWN good ground. As you have seen, when this wire DOES NOT have a reasonable path to ground, the machine shuts down in the same manner as what initiated your post. So, give it the best ground of all - a direct connection.