All of the electronics that aren't directly related to the high voltage system's operation are run off of the 12vdc system: the mirror motors, the wipers, fan, horn, displays, lights, stereo, etc. The main reason why it can get by with a small battery is that it does not need it to start the ICE in the REx, and obviously the electric motor doesn't have a 'starter'. IOW, the load on the thing is fairly small, and consistent, not a high peak draw like on a conventional ICE, especially when it's cold outside.
What sometimes happens with BMW vehicles is one or more of the control modules may not receive the 'shutdown' message from the main computer when you shut the car off. As a result, the static draw on the battery can end up much higher than the design parameters. I know on my other BMW that, if it is not started for a long time, it will gradually shut down some components to help make the 12vdc battery last longer. I wouldn't be surprised if that also happens in the i3. On my ICE, eventually, it will forget some of the stored profile settings (they can be restored with a USB stick if you've saved it). I've not noticed that on my i3 since it gets driven regularly.
I haven't looked at the programming for the i3's 12vdc battery, but on my ICE, the parameters do not include the option for a LiOn battery...only a traditional wet-cell lead acid and an AGM battery. On that one, it also offers a range of CCA values. That, along with resetting the battery age counter, are required for the charging system to be able to manage the battery properly.
Providing the proper max voltage value for the battery, and having the proper charging profile, will go a long ways towards maximizing the life of the attached 12vdc battery. If it doesn't know the type, it could be an issue. There are some LiOn batteries optimized for aircraft use, one of those MIGHT work, as, some of them have internal circuit boards to help mimic a lead-acid one.
Personally, I don't think a LiOn is a good replacement for a typical EV's 12vdc lead-acid battery, but there are some out there that could probably work.
2011 535i x-drive GT, 2014 i3 BEV