Hello all, I've read all the posts in this topic and found some wrong information.
I'll try to explain how the system works in short, if anyone has some questions, I will kindly answer them.
To start with, the 12V battery is charged ONLY with the high voltage system, by the power electronics that also drives the motor (the big metal block with the 6 orange wires connected to it next to the ICE) to be more precise.
There is no alternator on the ICE, so if you drive in E-mode or hybrid, it doesn't make a difference in charging the 12V battery.
This means the high voltage system must be active to charge the 12V battery, so only when driving or charging the HV battery.
The reason why there is only 13.1 or .2V is because the 12V battery is monitored by the gateway, it knows the charging state, so if it is above 80%, ther is no need to charge it, purely wasted energy to keep the system at 14V all the time. This is why the converter only supplies 13.2V to the system to just prevent the battery from discharging.
When driving and using the regen while braking, the system will be at 14V, all the modern cars do this, not only the hybrids. Actually most of them only have 12 - 12,5V while accelerating, when coasting or braking the alternator will start to charge the battery.
Why Sir_Ron_Norris' battery died, I haven't got a clue, but it isn't related to driving in E-mode or hybrid. Could be an driver error (leaving a light on, something plugged into the 12V socket,...), bad ground connection or just a faulty battery.
I hope with the new battery the problem has been solved.