It's the white plastic one that looks like a USB flash drive? I have one of those, and have repaired a few by swappng parts of "broken" ones. They really have great sound...
It works on my iMac running Mac OS X 10.7.4 and the latest version of iTunes.
The weakest part of that shuffle is the USB connector. It tended to wear out over time as you insert and remove it from USB ports. When I was fixing them, that was the most common fault. That could be your problem, and there is no way to fix it, short of taking it apart and replacing the USB connector and the thin ribbon cable inside that connects it to the logic board.
But you can try a few things. When you connect it to the Mac with Disk Utility running, does it appear in the sidebar as a "disk"? You can also run the System Information utility, which you can run from the About This Mac window, and see if the shuffle appears under USB. If the shuffle is recognized by either of those applications, that's good, because that means the connection is working. But iTunes is not seeing it for some reason.
You can try using the iPod Reset Utility.
This is only for the 1st and 2nd gen iPod shuffle. It does something like a Restore in iTunes, but at a lower level.