stronghold
A place that is very well protected and hard to capture.
A stronghold is a fortified place that's extremely difficult for enemies to attack or capture. Medieval castles were strongholds, built with thick stone walls, towers, and defensive positions that made them nearly impossible to conquer. During sieges, defenders could hold out for months inside a well-supplied stronghold while attackers struggled to break through.
Throughout history, armies fought to control strategic strongholds like hilltop fortresses or walled cities because whoever controlled these positions controlled the surrounding territory.
Today, we also use stronghold to describe places where something persists strongly. A mountain valley might be the last stronghold of an endangered species. A region could be a stronghold for a particular political party, meaning that party has deep, lasting support there. A coastal town might be a stronghold of traditional fishing culture. In these cases, stronghold suggests something that remains powerful and secure even when challenged by outside forces.
When someone says an idea has become a stronghold in their thinking, they mean it's deeply established and hard to shake, like a fortress in the mind.