I guess it's the power supply, from what I know external DVD writers are equipped with an AC power supply since it's power intensive when one is burning a disc.

BTW, I presumed you used a desktop and not your laptop, since most forums would not advise one to burn with a laptop, when the external generates it's power from the USB.
Another thing you should check is the desktop's USB plug; It should be 2.0 since a 1.1 plug (which is a common practice even with current motherboards that a 1.1 USB had been incorporated and a USB 2.0 is often optional)has difficulty supplying power even when one is just trying to recharge a mini IPOD. :'(