This is just a guess but considering the Ancient One specifically states ”together” I think it means that there has to be more than one Sanctum for the protection to work.
Wong: Together, the Sanctums generate a protective shield around our world.
Mordo: The Sanctums protect the world, and we sorcerers protect the Sanctums.
Strange: From what?
Wong: Other-dimensional beings that threaten our universe.
Strange: Like Dormammu?
Mordo: Where did you learn that name?
Strange: I just read it in the book of Cagliostro. Why?
Wong: Dormammu dwells in the Dark Dimension. Beyond time. He is the cosmic conquerer, the destroyer of worlds. A being of infinite power and endless hunger, on a quest to invade every universe and bring all worlds into his Dark Dimension. And he hungers for Earth most of all.
Strange: The pages that Kaecilius stole.
Wong: A ritual to contact Dormammu and draw power from the Dark Dimension.
This still holds true as the New York and Hong Kong Sanctums still keep the protection active when the London One falls.
Wong: The London Sanctum has fallen. Only New York and Hong Kong remain now to shield us from the Dark Dimension. You defended the New York Sanctum from attack. With its Master gone, it needs another, Master Strange.
Then when the Hong Kong Sanctum falls the Dark Dimension is able to come through because the Sanctums can’t work together, because there is only one.
Mordo: The Sanctum has already fallen. The Dark Dimension. Dormammu is coming. It’s too late. Nothing can stop him.
Mordo: When the Sanctum is restored, they will attack again. We have to defend it.