When the catapult of one of my heroes is destroyed (e.g. because of a sufficiently powerful Armageddon spell during a siege), how can I purchase a new one for him/her? Is there any town structure where I can do that, or any structure on the world map (like the War Machine Factory, which unfortunately only sells the other three: Ballista, Ammo Cart and First Aid Tent)? Or is this simply not possible?
The catapult only appears in siege combat, and can only attack castle walls and other fortifications. Every hero has one, it cannot be sold, given away, unequipped, or left behind, and if the catapult is destroyed during combat, it will reappear once the combat phase is over.
So from that I assume that you can't buy another one.