In Assassin's Creed Brotherhood, when one of your assassins dies, will there be another person somewhere that can replace him, or am I permanently short a man?
Yes, whenever you have slots in your assassin roster, you will find "assassin recruitment" missions around the world map. The most typical of these missions is to save a citizen who is being harassed by 4 guards. After a while you'll get used to the canned animation and dialogue that occurs when you win. "If I can help others as you've helped me - nods I surely will."
Destroying Borgia towers increases the number of available slots. Whenever your total assassin count is less than the number of slots you have available, new assassin recruitment missions will appear around the map.
Note that the new assassin will be at a low level, and you'll have to call them into battle or send them out on contracts in order to raise them back up again.
Assassins can be killed in combat if you call them in against overwhelming odds, and they can also die during contract missions, rarely even when the chance of success is 100%.