Ian, this does sound like a problem that has been mentioned here before
and which I suffered when I had a 300tdi. There are potentially a few
causes but the simplest one to check is the wire to the fuel cut-off
solenoid, which is mounted on the distribution pump.

The solenoid is located at the rear of the pump (i.e. end closest to the
bulkhead) and there is a single wire attached to it. The connection
tends to become dirty over time causing the connection to be broken
which, in turn,closes the solenoid and cuts off the fuel - it's how the
engine stops when you turn off the ignition. The remedy is simply to
pull off the connector and clean the male and female parts before
putting them back together.

Im sure others will be along with details of other possible causes - and
the alarm resetting suggests it could be the dreaded "spider" - but ths
is by far the simplest to eliminate from your investigations.

HTH