Sometimes they just don't get on. Get Walter Borthwick to tell you how to do AI. Pair the hen with another cock through the wires, bull system style, then AI her with Dileas sperm. A lot of bother maybe, but Walter has had success with it.
They can be let out for exercise before being fed. Exercise for around 1 hour. Shouted in as soon as they land. This is to prevent any possible contact with wild birds or their excrement. Whilst pigeons may not be able to catch avian flu, they can spread it by feet or feathers.