Saving a JPEG over and over again doesn't alter quality as long the compression rate is kept. I guess the algorithm just saves back the same RGB numbers again and again.
I don't believe this is true. I ran a test where I opened a TIFF, saved it as JPEG with Photoshop quality 8. I then closed the file, re-opened the just-saved jpg, "saved as" another jpeg with the same quality and new name, and repeated 4 times. The file sizes were:
Iteration 1: 1695 kb
2: 1670
3: 1668
4: 1669
The slight size increase at iteration 4 is a bit of a mystery, but you can see the file size goes down with each re-saving of the file (no changes were made to the image). Something is being lost.