With the availability of modern satellite and data transmittion technology, the possibility of continual tx of FDR information should be possible.
This looks like a good solution but there are issues in the details. One of these is that the satellite connection is easy to manage when the aircraft is flying in a normal attitude and with normal electrical power; it is not so easy in an emergency situation. You could end up with the remote recorder missing all the most interesting data because the connection was lost. Designing a system that will work in extreme conditions is much more demanding.