to update:
I downgraded a workstation to version 10.1 and the replica synchronized successfully. After this successful synchronization, I tried again from the 10.2 client, and it worked (but no changes to transfer). I then added a record to the parent geodatabase so there would be changes to transfer, and synchronization from 10.2 was successful.
There are two replicas related to this data--one is a file geodatabase, the other is an SDE geodatabase, both one-way. The same issue presents in both.