How long are the stock iPhone charging cords supposed to last?

That really depends on how well you take care of them. I've had most of mine for years. The only one I remember going back was one that, by virtue of where it was plugged in on my desk at work, used to get slammed in a desk drawer rather regularly.

Make sure never to wind them up tightly. Don't bend them sharply right near where the cord attaches to the connector. Always pull them out by the connector, not by yanking the cord.