<p>Most developers understand the concept of <a href="http://en.wikipedia.org/wiki/Wicked_problem" rel="nofollow noreferrer">wicked problems</a>. What's a good analogy to use when explaining this concept to project managers?</p>

Every changing requirements lead to an impossible to manage design. Just send him here:
Winchester Mystery House
. The house is filled with staircases to nowhere and doors that open to brick walls. It was built exactly as spec'd, but isn't really what you'd call usable.
Of course up here in New England a "wicked problem" is one that requires a wicked good engineer to come up with a wicked clever solution :)