Should not the CVR if not the FDR have an internal battery to keep it running for say 1 hour after power loss? Totally separate from on board power, and with recent battery technology we're not talking a great lump of a battery.
So that you can still "pull the C/b" following an incident run power to it from two systems, batt. only kicks in if both power inputs go dead, if primary goes dead it assumes you have deliberatly disconnected it and stays off.