Quote Originally Posted by ReiseReise
They can only recruit a crusade army for 10 turns, so generally by the time they reach you and you destroy them, they cannot build another. If they do not make progress towards you every turn, they will gradually disband, so if you have not seen them after about 20 turns, i would say you never will. Or you can use toggle_fow in the console (press ~) to turn the fog of war off and see if the crusade armies still exist or not. Use toggle_fow again to get your fog back.

Side note: I use toggle_fow once every few turns, I try not to cheat with it, but I get great enjoyment out of seeing how the AI is doing against itself. Its usually like watching two drunks in a barfight... it probably started for no reason and neither party has any ability to fight effectively, but every once in a while one will stagger, wind up a punch, stagger again, almost fall over, finally throw the punch, the other one still won't see it coming and gets clobbered, falls over, gets back up and returns the favor in the same manner. Repeat.
The losing of troops for not going towards the objective only applies to the player, not the AI. I've had AI stacks of crusader knights/sargents just sitting in my lands for 15 turns waiting for the crusade to be over to attack me.....

Yes, crusades can only be joined in the first 10 turns, but take note if you don't kill the general (as in he flees like a coward) he can always recruit himself some more troops if theres some in the region. There seems to be a time limit as well for crusades in general, but its something silly like 50 turns, because i've had a few young generals sitting outside the target city for a very long time and had the pope call off the crusade due to something about the cost of lives being excessive or something....