When a Crusade is called (or a Jihad for that matter) the player and AI have 9 turns in which generals with at least 8 units (including themselves) to join. Those crusading generals are what keeps the crusade/jihad alive. Until the crusade is successful, generals are killed in battle, or die of old age, the crusade will continue. These generals, as long as they are alive, can continue to add new troops to their crusade; hire new mercenaries; and hire new crusaders. If you want to end the crusade/jihad, build and army and go out and destroy them or build up an assassin(s) and assissinate the generals. But as long as they are alive and the objective hasn't been completed, the crusade will continue.

Not sure if pope dieing ends all crusades, or only crusades vs catholic factions/cities.

Note: Playing currently as the turks, I've had 5 crusader armies throwing themselves at Constanople for the last 27 turns. I've succeeded in killing on one of the generals and the other four are still throwing themselves at me, rebuilding their armies, and throwing themselves at me again. The good news is that my troops in the city are now all silver with a few gold chevrons appearing. Great way to chew up enemy troops for experience. Since its free upkeep of their troops through, it lousy at bankrupting them.