When I messing around with my replacement Key a while ago, I had the similar situation with the "immobilizer fail" displaying,
that is where the RFID unit is not reading the chip [that is in the Key Head]
As I had to program it in, to stop that from displaying.
There is 2 stages of RFID in VE's
- Is the ID Chip in the Key Head [Non Flip Head, and Flip Key Heads]
- Is the Remote side of it, to unlock and lock the car, and all the other smart stuff it does in the background, based on your level of vehicle variant.
Based on that, there is 2 Area's of the BCM that the key needs to be programming to make it work.
But with your situation,
Does it happen with Both Keys [assuming you have 2 keys], if it does, I am guessing its the RFID receiver could be at fault, which is located around the ignition switch by memory.
or
If its only happening on one Key, I am guessing chip could be faulty.
That is where you would need to get a new Key Head, get the Key cut [that's if its a non flip Key],
but if you have a flip Key, get a flip Key Head, you can swap the Key Blade that will/could save you $44 > $80 depending where you go.
Either way, the new RFID chip will need to be programed into the 2 Area's of the BMC,
But your existing Remote still should work.
I had a complete opposite situation before purchasing my replacement Key
The Key would work, and the car would start,
But the remote unit failed, and it wasn't the battery, as I tried 2 new Batteries,
Hence the reason I purchased a new key and had the similar issue.
As for the service, it could be co-incidental, unless it does need a service,
How many K's has your car done ?
On the other had, a immobiliser issue will not activate the MIL lamp, so I would get your car scanned to see what it is doing, or in this case Not doing.
then take it from there.