4th gen is still the current shuffle model, so if it's less than one year from purchase date, it's under standard warranty.
Since light does come on initially, the shuffle seems to be getting power. The cause is probably not a faulty USB docking cable. You're using original ultra-short docking cable that came with it, correct?
It is possible that the Mac's USB port is not providing enough power (to charge shuffle's battery) for some reason. Do you happen to have a USB power adapter, like the one that comes with iPhone or other device? If you do, put shuffle's power switch in OFF position, connect docking cable to power adapter, and plug in your shuffle there. See if shuffle's light is different for a power-only connection. (Normally, you should see solid orange light while charging and solid green light when fully charged, with a power-only connection.)
If you get the same red light from a USB power adapter, the most likely cause is a worn out battery that can no longer charge.
If you can't do that test because no USB power adapter, shut down (power off) the Mac and disconnect all USB devices. You can leave standard USB keyboard/mouse connected, if used. If your Mac is a laptop, connect its power adapter (so it's not running on battery power). Put shuffle's power switch in OFF position. Start up your Mac, run iTunes, and connect shuffle to a direct USB port, by itself.