This is where many people get confused with the remote keys and the 3 features/systems that are involved. I written about this for years so I'll try to explain it. The biggest mistake is that there's only 1 feature activated...when actually there are 3 features/systems involved in the remote keys and they are all independent of each other but do work in conjunction with each other:
- EWS - immobilizing system: shuts down starter/fuel injection/ignition
- DWA - arming/disarming of the anti-theft alarm siren system
- FZV - remote locking/unlocking activation of central locking system
EWS/DWA/FZV all get or send some type of data/info to or from the GM...this is one control module that they all communicate with...thus it is also one of the things that makes people think that the key only does one thing. EWS & FZV (central locking) communicate by way of the GM & K-bus in that it tells EWS when the engine is NOT running...thus the doors can be UNLOCKED. But that's all...the procedure to reinitialize DWA & FZV remote operation...it has NOTHING to do with the EWS communication that immobilizes the car. Again, these a 3 independent systems that only work in conjunction with each other.
TX5 asked about how does the key start the car when the key's batter is dead...I think you found your answer in the EWS info you posted. The EWS transponder gets powered thru induction...it is powered by the Ring Antenna around the ignition switch...unlike the FZV & DWA transitted RF signal which requires the use of the battery inside the key. That's why we always tell people that a dead key battery has no affect on the key to be able to start the car. The internal key battery is not needed.
Resyncing EWS...I mentioned this in my previous reply. When the key was left in ignition position 1...EWS communication is occuring. And when the car was left in this condition and the battery died...this is where the "deviation" may have occurred in the rolling code tables.
The only way to resync EWS is with proprietary hardware/software...there has to be some communication with the communication BUS. Other that BMW DIS/GT-1...I think Ive read in the past that INPA can resync EWS.