BC is an ongoing ability, just like the Protect Forts from Priests or the Di Sites. Caesarea Phillipi protects NT EC's in your territory from discard by opponents, but once they enter battle, they can be discarded. The small difference is the decrease ability, which can be instantaneous or ongoing. It has been ruled that increase/decrease abilities on ongoing effect cards (like artifacts, placed enhancements, etc.) are constantly targeting, but the effect is not permanent. This is to prevent the idea that if I reactivate PwD every turn, I don't get to "stack" the 0/2-3 decreases; same with Crown of Thorns. Thus, just like if a character that leaves play is no longer affected by PwD or CoT, a character that leaves territory is no longer affected by Broken Cisterns.
Did that help? Let me know if anything else needs clearing up.
