Brian,
As well as the latest software tweaks from your end, I investigated the possibility that the Arduino may have been sensitive to ‘reflections’ or ‘echoes’ on the bus line on which I have my sensors (at this stage just DS18B20 temperature sensors - others types to come later). To this end I bridged the bus, at its furthermost point from the Arduino, between the positive line feed (5V) and the data line with an appropriate value resistor. [The 1-wire sensors are being run in powered mode - not parasitic mode.]
I am pleased to report that I have had no drop outs since. Running problem free, at this point, for nearly 60 hours straight.