[JimD]

If you do not register the battery, tell the car's computer you put in a new battery, it continues to think it is charging an old battery of the size and type that used to be there. As I understand it, old batteries require more charging than new batteries. I have no idea if that is higher voltage, or lower voltage for longer, or what. But charging a new battery like it is an old one has been reported to shorten it's life.

BMWs also do a minor hybrid type thing by charging during braking. The purposely do not fully charge the battery so there is some headroom to goose up the charging when you brake. That helps slow down the car and also uses a little of the kinetic energy of the car to charge the battery. If the car doesn't know what size, type and/or age of battery it is charging, it may also mess up that process.

I agree that issues with date/time disappearing seem unrelated to battery registration. I guess it could be related if the lack of registration caused the car to deliberately undercharge the battery excessively. I am not sure exactly how that would happen. Installation of a really big old battery?