Hello Tal and thank you.
I've been thinking that all of these issues started after the 3G modem upgrade. I had no issues at all with the 2G modem and everything worked with it.
With my limited information on the issue, I see two possible causes:
1) The 3G modem hangs because it tries incessantly to connect to Nissan's Carwings backend - but the back end is down - and it doesn't enter sleep mode until it does. Seeing that Carwings has had so many issues since the start of the year, that is a possibility. However, I have checked with 3 other Leaf owners and no one else had seen Carwings issues while I was.
2) The 3G modem hangs because the 12V battery drops below a certain voltage level. If there were something broken with the 3G modem, it would always stay on and always drain the 12V battery, but it doesn't. As I had mentioned above, I replaced my 12V battery with a new one straight from the store. That new battery got drained a number of times until I took it out and charged it separately with a proper charger. After it worked for a few days, I left the car alone without starting it for 5 days straight. No issues and Carwings worked every day. This gives credence to the guys claiming that the Leaf is not properly charging the 12V battery.
Yes, it does sound like a chicken<>egg thing. Does it drain the battery because Carwings backend is not available and the modem keeps awake trying or does the 3G modem hang and doesn't enter sleep mode because the 12V battery is below expected voltage?
BTW, my car started throwing all kinds of strange errors in the dash and DTC codes when the battery was below nominal voltage. All of those went away after charging the battery.
PS: happy Father's day!