Copy Protected Floppy Disk-How to backup

I have a floppy disk that is a key disk for a program. When I install the program I have to insert the floppy to get my legally owned 50 user licenses. If something goes wrong and I have to reinstall, I have to get ahold of the software manufacturer to get another key disk and they read me the riot act bla bla bla.

I've tried copying the floppy, but a copy does not work. It has some kind of copy protection. Here is some infos about the original disk:

1,457,664 bytes total disk space.
22,016 bytes in 3 hidden files.
134,656 bytes in 3 files.
9,216 bytes in bad sectors.
1,291,776 bytes available on disk.

512 bytes in each allocation unit.
2,847 total allocation units on disk.

Once the disk has been used, only one visble file has been altered and it will not work again.

I searched the forum to see if I could find a high-end floppy copy program that will get the bad sectors and all. I came across this post, but it looks like the attachment has been deleted.

If anyone can help me I'll be thankful.
Years ago I had a program called CopyIIPC... kind of a CloneCD for floppies. I don't know if they still make it or not.
Made more powerful with an "option card".

If you have an old copy of it (I do), it fails miserably on modern PC's - it seems to be unable to run correctly on anything faster than a 386

9216 bytes is one track, so it has a bad track, or possibly a track which is marked bad but actually carries concealed data.

Is it one of these where you can uninstall the licence back to the floppy (assuming the hd didn't crash or something!)

Googled up a few somewhat questionable resources.

Yes I can put the license files back on the floppy if I plan ahead.

Thanks for the ideas guys. Keep the info coming.
A good app called Floppy Image may be just the thing you need - get it here:

Create image files of floppy disks and back (for backup, shipping or transfer). Save the image file compressed, uncompressed or as a self-extracting exe. Add descriptions to or convert your old image files. Supports DMF and other non-standard formats. Logically recreate bad sectors when writing floppy disks, allowing for an exact duplicate of your source disk to be created. The self-extracting exe can be fully customized with a picture, license agreement dialog and a text with instructions. Full support for drag-n-drop.
Thank you Slippery. After trying many different programs, some ancient and running in DOS, FloppyImage did the trick and it runs smoothly in Windows.