Hello Damian,
I refute your suggestion that heating from cold each time would use more gas than maintaining the water at an elevated temperature. I propose to indicate that heating from cold uses less gas.
According to Truma's Web site the current model uses gas at a rate of 120g/h and raise water from 15 to 70C (a rise of 55C) in 34m. Whilst not strictly true (see note 1) this suggest that it takes an average 38s/C or 1.25g/C.
I have been unable to find any reference to the heat loss rate of the Truma Boiler, but I consider .5 to 1.0C/hr you suggest to intrinsically very optimistic. Even a sealed glass vacuum thermos flask loses more than that! By comparison Carver used to quote the similarly specified Cascade 2 heater would run for about 6m/hr in maintenance mode.
Based on this simplified calculation, over 6 hours the heater will cycle on for about 36m which is the about the same time as heating the tank from cold.
So based on this simplified example if hot water is not needed for 6 or more hours, it will use more gas if it is left on but that assumes the tank will cool by 12C per hour every - which it wont. The rate of heat loss diminishes as the tank gets cooler, and it wont fall below the habitation temperature. So after 6 hours the tank won't have cooled to 15C but more like only 20C so it will take less time and gas to reheat from 20 to 70C
Note 1.
The situation is actually slightly worse than outlined above. The fact is that the heat transferred to the water is affected by the water temperature. Cold water will accept heat more readily than hot water. It is almost the case that water at 15C will heat almost twice as quickly to 16C compared to water at 69 to 70C, and the rate of change is not linear but exponential.
If viewed on a graph the temperature against time curve will be like the leading edge of a sharks fin, steep at the root becoming increasing shallower the hotter it gets. Similarly the cooling curve is steep at high temperatures and becomes shallower as it approaches ambient.
The maintenance cycle all occurs at the top of the graph, where it takes more energy input to raise temperature and where the most rapid cooling occurs.
So if the average temperature rise is 38s/C, then at 67 to 70C it will be almost 60s/C. This means the maintenance heating times will be actually longer than I have calculated above, meaning it uses substantially more gas than I have indicated.
All in all if the hot water is not going to be required for more than about 20min there will be a slight economy gain by turning the heater off. The economy gain will increase the longer no hot water is required.