Many of the parades take place more often as the Palio gets near, so in June and in July for sure. I am sure they practice during other times of the year but those are not on any specific schedules as they really aren't for the public and are considered practice sessions in preparation for the Palio events. Remember the Palio is a beloved local tradition and not something put on for show of visitors, so they aren't too keen in posting anything about what they do so that others can get involved. Each contrada considers itself a community and fierce loyalty is the norm -- people from Siena first of all belong to their contrada, then only after consider themselves Sienese, lastly Italian ;-).