Red Hat Directory Server 8.2 replication halt, error Consumer failed to replay change (uniqueid (null), CSN (null))

Issue

LDAP Replication stopped working, with various errors like:

[22/Jan/2014:01:00:09 +0000] - Backup finished.
[22/Jan/2014:07:53:17 +0000] NSMMReplicationPlugin - agmt="cn=replica4-to-replica5" (10:10686): Failed to send modify operation: LDAP error 81 (Can't contact LDAP server)
[22/Jan/2014:07:53:17 +0000] NSMMReplicationPlugin - agmt="cn=replica4-to-replica5" (10:10686): Failed to send update operation to consumer (uniqueid 150d2e82-591b11e1-92bcf376-dd55dbc4, CSN 52df7e28000000220000): Can't contact LDAP server. Will retry later.
[22/Jan/2014:07:53:17 +0000] NSMMReplicationPlugin - agmt="cn=replica4-to-replica5" (10:10686): Consumer failed to replay change (uniqueid (null), CSN (null)): Can't contact LDAP server. Will retry later.
[22/Jan/2014:07:53:17 +0000] NSMMReplicationPlugin - agmt="cn=replica4-to-replica5" (10:10686): Warning: unable to send endReplication extended operation (Can't contact LDAP server)