The landmarks will not heal over time, they are just 1000+ year old buildings that cost a lot of florins (The Colosseum is 1425 years old in game at the start). They are simply part of purchasing (rebuilding is the wrong word in this case) all of Rome which gives you a trophy on PS3? (no achievement on 360) and the auditore cape which keeps your wanted level down to 0% all the time. They are also where you find the 6 temples of Romulus and the subject 16 Puzzles.
After purchasing the landmark you should see a brief cut scene that shows the landmark being renovated. Purchasing landmarks increases your income and contributes towards a trophy. They can be quiet expensive so perhaps you do not have enough money to buy them.