Handbrake Stops Prematurely

you can try mac the ripper (or similar, not sure if it still works or not).
It will rip the entire disc to your hard drive, then you point handbrake to that image.

I haven't used it in a while, but it used to be a little more forgiving than handbrake by itself.

Here is what you can do. Save the file that Handbrake encoded until it fails and note the time at which that occurred. Now restart Handbrake and once the DVD is loaded, change the start time to a few second (or minutes) after the failure point. Now Handbrake should encode the remainder of the DVD in a second file. You can combine the two files afterwards or leave them as they are.

This works reasonably well if there are only one or two damaged sections in a DVD. If you have multiple damaged sections then you may want to contact a professional service that recover the data for from the disc for you.