Performance Point Dashboard Designer Won't Launch for a New Installation

We've been observing a problem in a few PerformancePoint installations that we've done recently. You create a new Business Intelligence Center, and then you want to create a new dashboard. You navigate to the PerformancePoint content library and select the Add new item link. You get the "Loading Dashboard Designer" Ajax prompt, but then nothing happens. If you open up the ribbon, and try to create any of the PerformancePoint items, you see the same behaviour.