It's been discussed to have the CVR and the FDR 'mirror' each other - i.e. have both record the same data. As memory has gotten smaller and cheaper, it's now practical.
It would require some up-front expenditures to add the capabilities, and some wiring changes to the aircraft, but it's certainly 'doable'...
The biggest drawback to 'real time' data download is recurring costs - the satellite band width doesn't come cheap.