The Alfa system sounds very much like the Mercedes one on the 159/Brera. The 147/GT/156 keys can be reprogrammed but the 159/Brera ones are 'one time' flashed as a set. Each car can have up to around 7 or 8 keys. After then the car needs a new Immobiliser/EIS/Everything.
The keys in the Mercedes also start the car with no battery in the key, so if your battery is low, you enter the car with the key blade and insert the key body into the EIS, which then energises the key which has a coil in it producing enough power to run the key for recognition.
I have yet to try this on mine with the battery out but reckon it would work.
The issue with the mercedes keys was the coil in the key used to loose connection with the PCB after the key was dropped or through time, making it useless for starting the car. Resoldering fixes the issue.
Ryan/BigGinge, I suggest you check your keys to see if one has a similar issue. There was a 'how to' on here somewhere recently explaining how to dismantle the key body.
In the meantime I will see if mine definitely work without batteries.