Whether they be 30-pin or Lightning, Apple charging/syncing cables are not known for their durability. They are known, however, for lasting about three to six months longer than they should, until the point where you look at the exposed wires with incredulity and hope that an electrical fire doesn’t start.
Or, you could opt for the Kero Lightning Nomad Cable. It’s a USB 2.0 to Lightning connector, with a flat, flexible 3” cable that is pretty thick, and will not fray like your old white (now dirty grey) Apple cable. There’s also a handy loop on the USB cap that you can fit onto your keyring. It’s certainly a more convenient travel companion than the standard charging cable, and will be much more durable, too.
The Lightning Nomad Cable comes in blue and white, but the blue model is currently sold out. The white model is selling from Kero now for $25. There’s also an identical version of the cable currently in Kickstarter for a USB 2.0 to Micro USB connector.