The scenario uses the 5-Pointed Sun location, which never permanently closes. In order to win the scenario you need to close all locations. The scenario rules allow you to attempt to close a location if you find 1 barrier after performing the mandatory end of turn examination. So is the intention of the scenario is that you use the scenario rules special close condition to close the 5-Pointed Sun after all the other locations are closed?
We just played this on Friday. We assumed that this could work, since otherwise the scenario is unwinnable; that is, we figured we can attempt to close via henchman, barrier, or exhausting the location, and then if it's the only one left, we figured we might win before triggering the when permanently closed power to never be permanently closed. I don't think that's standardly correct for order of operations, but otherwise there's no winning.
EDIT: Aha, location FAQ!
The Five-Pointed Sun was FAQ'd. You can now close it if all the other locations are permanently closed. So, in a scenario where you must close all the locations to win, you are forced to save it for last.