The Airbus SD documentation states:
The CVR is automatically supplied with 115VAC when the aircraft is in one of the configurations given below:
- In flight with the engines running or stopped
- On the ground with at least one engine running
- On the ground during the first 5 minutes following energization of the aircraft electrical network
- On the ground up to five minutes after second engine shutdown
I don't have time to dig through the full electrical schematics, but power is certainly more or less directly derived from the battery via an inverter.
So, unless battery power was lost, I would expect the CVR (and by implication SSDFR - I don't have that schematic to hand...) would remain powered.