Couple of things I'd like to add to this thread... Sorry but I do go on a bit...
I suffered the "no EV mode" problem last Saturday and so took it into the local dealer yesterday (Thursday) to have it looked at. The technician said there was a fault on one of the ECUs and Peugeot diagnostics recommended 13 updates which took him over 4 hours to do as they can only be done one at a time. My total battery range has now increased from 22 miles to 33. A drive over to the next town this morning for petrol has confirmed that the new range is pretty accurate. It's on charge now and I'll see if it's any lower when it's finished.
It does seem smoother than before but the only real noticeable added difference I can detect is the piped engine sound in sport mode which I didn't have before (I hate it!) and sport mode also feels a little more taught. I pleaded for a copy of the updates list and though he was happy to show it to me, he said he wasn't permitted to give me a copy. I tried...
The other point is to do with the starter and accessory batteries. I was concerned, like others. that if the ICE is never used, the starter battery is never charged, so I asked when I bought the car how these worked and was told its NOT from the ICE via an alternator but by a DC transfer unit from the traction battery. Now, in my first week of ownership. I fitted a Ctek battery monitor to the accessories battery under the boot floor (couldn't get to the starter battery neg terminal under the bonnet), and have monitored the state of charge (SoC) while the car is stationary and turned off, both with and without the traction battery being plugged into the wall charger. For example, I collected the car yesterday evening and it read 66% SoC (the car had been sat in the service center all day getting the updates done, ignition on but engine off) but within 2-3 hours of getting home and having plugged the traction battery in, it was back up to 100%. BUT, the traction battery didn't start charging till half past midnight because I had it set to deferred charge.
So in a nutshell, the starter and accessories batteries DO appear to be maintained by the traction battery, meaning the car can be driven in EV mode almost indefinitely. That being said, I'm sure the ICE needs to be turned over from time to time to maintain it's optimum health.
Finally, I don't know if I have the 3.7 or 7.4 kW charger fitted to my car, and I ordered a 3.7 kW wall box as my house is oldish and was concerned about the strain on the old wiring. My car charges from 0-100% at a charging speed of 16 - 18 mph, and takes 1 hour 50 minutes.
This is just my experience and my observations of my car Hybrid4 300 GT. Others' experience may differ.
Edit: Just finished charging and it's up to 33 miles again. I'm going to set up a spreadsheet to record range, temperature, date, etc...