If the light does not stay ON (and also the red color), that can mean the battery is not able to charge or the shuffle is not getting enough power from the port.
As a test, shut down (power off) the Mac and disconnect all USB devices. You can leave standard USB keyboard/mouse connected, if used. Put the shuffle's power switch in the OFF position, if it is currently ON. Start up the Mac, run iTunes, and connect iPod to a direct USB port on the Mac by itself.
As another test, if you happen to have a USB power adapter, like the one that comes with iPhone or other device, connect the shuffle's docking cable to it, and connect the shuffle there. Does the shuffle's light come ON? It should be solid orange (amber) when changing and become green when fully changed.