I have seen that nobody design a reversible semi-fragile audio watermarking. However, there are many reversible semi-fragile image watermarking specially for medical images.
Try lossless semi-fragile audio watermarking mechanism. It is possible to reverse it without loss. There are many research papers on it. One link is attached herewith.
A reversible watermarking requires high payload on the medium. If the medium allows high payload without affecting the perfectibility, i dont see any reason why it cannot be done.