It could be a problem with the USB port, the USB cable, or the shuffle itself.
For the USB port, it seems to be working because it works with your other iPod. However, if you have other USB devices connected at the same time (such as your other iPod), I would shut down (power off) the Mac and disconnect all USB devices including hub. Do this to Reset the shuffle
(also, if you can note which shuffle model you have and include that info if you need to post back.)
Start up the Mac, run iTunes, and connect the shuffle to a direct USB port on the Mac This is to test if there might be a power-related issue or USB conflict between devices.
To rule out faulty USB cable as the cause, if possible, try a different USB cable, or try the one you have with another shuffle.
Does the shuffles stay connected long enough for you to go to its Summary screen in iTunes, to make setting changes?
If you can view the shuffle's Summary screen long enough, look at the setting for Enable disk use. If it is currently not checked, see if enabling this setting makes a difference. This will keep the shuffle's disk mounted by the system continously, until it is manually "ejected" when you want to disconnect the shuffle.