I have been able to recover from a broken Live Script. Basically, my live script file was corrupted from an abnormal termination of MATLAB. When I tried to load the live script, I was able to see my live script code to pop up, but after the code displayed, I got the "Error Loading ...." popup.
Here was the fix.
This was how I diagnosed the problem. I opened up the live script (the mlx file) with unzip from the command prompt. The mlx file acted like a zip file as far as unzip cared. A directory tree was created. In the "matlab" subdirectory. I saw the output.xml file was enormous and likely corrupt.
This is how I fixed my corrupted mlx file. I created a blank mlx file in MATLAB. Then I used 7 zip to open up the blank mlx file, and copy the contents of its output.xml file. So I had the "fresh" output ready to paste on the clipboard. I then again used 7 zip to open up my corrupted mlx file and I edited its output.xml. I did a "select all" in the editor and replaced it with the fresh output.from the clipboard. I saved it. 7 zip asked me to confirm if I was sure I wanted to update the archive and I said yes. And voila, I was able to open the corrupted mlx file.
Now here's the rub: I had to fix what the live script was doing before I ran it again. The corruption of the output.xml occured because of the abnormal termination of MATLAB. That happened because I pushed the limits of an ODE solver too far and it was generating so many error messages that the link between the UI and the backend of MATLAB got detached. That is why I suspect MATLAB hung. So I did not want another such hang. I had to loosen the tolerance I was using in the ODE solver.