Why is Cloudforms 3.X replication backlogs growing astronomically?

Issue

After various reboots and a dbsync:reset, backlogs are still growing on one of customer's replication worker appliances.

[----] I, [2014-08-06T17:03:15.116596 #1834:8e6804]  INFO -- : Q-task_id([log_status]) MIQ(MiqWorker.log_status) MiqReplicationWorker: [Database Replication Worker] Worker ID [10000000017062], PID [1895], GUID [7c53e60c-1d7b-11e4-9f1f-005056aa77d1], Last Heartbeat [2014-08-06 17:02:52 UTC], Process Info: Memory Usage [85454848], Memory Size [350298112], Memory % [1.39], CPU Time [1458.0], CPU % [0.21], Priority [30]
[----] I, [2014-08-06T17:03:52.753430 #1895:dd6814]  INFO -- : MIQ(ReplicationWorker) Replication Status: Current Backlog=[5541], Added=[1326], Deleted=[0]
[----] I, [2014-08-06T17:06:52.951469 #1895:dd6814]  INFO -- : MIQ(ReplicationWorker) Replication Status: Current Backlog=[5817], Added=[137], Deleted=[0]
[----] I, [2014-08-06T17:07:53.032432 #1895:dd6814]  INFO -- : MIQ(ReplicationWorker) Replication Status: Current Backlog=[6014], Added=[197], Deleted=[0]