There were a few suggestions that you did not clarify (if you tried them or not). At this point (based on what you have stated), the problem could be on the iPod or it could be the USB connection to the Mac. It could also be the USB docking cable, but since it connects initially, it is probably OK. You should rule out a problem with the USB port on the Mac.
I suggested shutting down (powering off) the Mac. Did you do that, and then start it back up? If the Mac is a MacBook, you may need to do more because it has a battery.
I suggested disconnecting all other USB device (except for standard keyboard and mouse if used), and connecting the iPod to a direct USB port on the Mac (by itself). Did you do that?
You can also try connecting another device, preferably something similar like a USB flash drive, to the USB port you used with the iPod, to confirm the same thing does not happen and it works properly. Does it connect and stay connected?
Those steps will help confirm that problem is not the USB connection (on the Mac side).
To do a Restore, it needs to have a stable connection, so that the iPod appears in iTunes. When you select the iPod in iTunes, the screen that appears is the iPod's Summary screen. But if the iPod does not stay connected in Disk Mode, doing a Restore will not help. In Disk Mode, the iPod should act like it is a storage device.
Try this... Connect the iPod. Instead of running iTunes (quit iTunes if running), run Disk Utility. Does the iPod's disk appear in the Disk Utility sidebar?