What if the strength of the circle is based on street traffic around the road outside, and construction blocks that road off for a while?
There's something from the Exalted setting that has a really close relation with this idea: The Order Confirming Trade Pattern.
Without getting too much into the background (and thus way off topic), it's a pattern of trade networks designed to keep back the chaos that eats at the edge of the Creation. That chaos is filled with monsters and all sorts of nasties that want to rip the world apart, you see.
The many, many people that walk the roads of the Order Confirming Trade Pattern each grant a tiny amount of themselves to it. Although this doesn't take anything remotely measurable from the individuals, multiplied by all the people that travel the roadways it builds tons of power. All that power is concentrated into using the Pattern to hold back the tides of chaos.
This could be something really similar.
So each person traveling on one of the circle roads gives up a tiny bit of their life force. When I say tiny, I mean they need like 5 seconds of extra sleep to make it up, or something equally harmless. But with all the people that drive one of the roads every day, it builds a rather large charge.
The way that the area is constructed, each of the outer concentric rings channels the power it collects through one of the spokes and into the inner ring. Since there are several spokes, it doesn't really matter if one is blocked, because the excess power will just flow down another spoke.
But what indeed happens if the whole area is shut down? It's true that a magical battery that big could have built up a really epic charge. However, it's not infinite. It can be used up. And when it's gone, that's when it can be broken into/ out of.
That's actually a really interesting idea to run as sort of background noise. Come up with some innocuous Theme related to traffic and the roads, then mention during several stories the increasing amounts of construction. Play it up as flavour, and occasionally make it interfere with getting somewhere on time.
Then spring a major story involving whatever it is being kept in/out of the church. As soon as they understand the nature of the protection circle, the players will suddenly realize that you've been building up toward this for several stories.
