Copying what I can from bit rotted disks?

["Jayson Smith" <ihatespamratguynospamplease@insightbb.spamsucks.com>]

Hi,

     I have one disk in particular that has sadly become a victim of bit 
rot. It's a flippy with various music programs on both sides. It loads the 
Textalker software, and was part of a set of talking disks with lots of 
public domain software on them. It is DOS 3.3. I have no idea who put 
together this collection of disks, or I'd ask if anyone has a replacement, 
as well as any other disks in the set I don't have. There were probably over 
fifty of these disks. In any event, on this particular disk, both sides have 
been victimized by bit rot, and some of the programs are not copyable. I 
assume, once bit rot has occurred, there's virtually nothing that can be 
done to try to bring those files back from the grave? If that's true, than 
I'd love to find a program that would take the disks, and copy all the files 
it can to another disk. Possibly retry a few times if an error occurs, but 
if all its efforts are for naught, don't stop the process entirely, just go 
on to the next file, and make a notation of which files could not be copied. 
Obviously, FID will copy all files, but when it hits an I/O error, it stops. 
I can manually copy each file, making a list of those that can't be copied, 
but surely there must be a more automatic way. Something you can just set 
and forget, and when you come back, it says, "I copied this disk, I could 
not get the following files..." Any thoughts?
Jayson