xDB Replication Server performs replications asynchronously. The systems hosting the databases do not always have to be running continuously in order for successful replication to occur. If one system goes offline, replication resumes when it comes back online if there is still pending data to replicate.
In addition you can create a schedule for your replication system. xDB Replication Server initiates and performs replications regularly according to the assigned schedule. This allows you to run the replication system unattended. See Creating a Schedule for directions on creating a schedule.