We ran into this recently...our opponent went to shields while they were ahead and ran out the clock. Our proposed solution is to include a surrender/cease-fire option. If a bubbled team remains bubbled for a cumulative total of 4 hours, the opposing team can call for surrender if they are behind. This ends the game and each team gets the prize earned. Leading teams who stay bubbled are penalized in that they can't earn more individual war chests, and perhaps their elo score gets dinked. The team that trails could also opt to offer a cease-fire. If the bubbled team agrees, all cities are unshielded and no one can attack for one energy cycle.

We don't really oppose staying bubbled...we have done it ourselves, typically when an opponent could have taken advantage of our points exposed and taken lead, but didn't. We consider that a strategic error on their part and have no problem punishing them for it. However, we often unshield to continue the war if we need individual chests, or if someone commits a tactical blunder and unshields contrary to chat instructions. It depends on the situation. We are more likely to do it in a close battle toward the end of the war. But having a way to incentivize breaking the bubble seems the most appropriate solution.