Can ships not afford a satellite uplink for continuous telemetry? Compared to the $1000s/hr of diesel they burn, the data can't cost much.
The question isn't "can the ship support continuous telemetry" but "does it generate more value than it costs". And I'm not sure it does. Also, since the crew survived, why are they so concerned to get the voice recorder? Is it just because of the recorded alarm information, and if so why keep referring to it as a voice recorder and not a black box.
Just like with aircraft accidents, the conversations can provide as much (or sometimes more) value as the data. It gives you insight into decision making, details that may not be recorded in the data ("I was just in area XYZ and I saw sparks coming out of one of the vehicles"), etc.