In reply to purplemonkeyelephant:
depending on the fault it may be better to copy it all in one go as the head starting and stopping reading may be causing more damage rather than any continuous operations.
It may be the best thing to image the drive all in one go as most imaging applications will treat the drive as though it were one big file though it will have to stop reading for a bit to write the contents it has buffered in ram or as any io bus involved gets "saturated". You can minimise this by taking the drive out of its external housing and mounting it in the PC as you would any hard drive (you can get an adapter for it if is a 2.5" drive.
There is also the possibility of some applications being able to recover corrupted bits of files from that image but that is really best done by someone with experience in doing so.