If you allow them to live forever all the factions will end up with super elite spies / assassins with hundreds of years experience.
I think ideally the spy network would be abstract, not actual characters moving around the map. The more money you put in, the more effective it is. Cut off funding, it goes away.

Its just a way of allieviating some micromanagement and getting a few less characters off of the (now very crowded) map.