Occasionally FlowFiles appear to get "stuck" in a Load-Balanced Connection

When a Connection is configured to Load Balance across the cluster, we have seen reports on the mailing list of FlowFiles getting "stuck". The connection shows that the data is being actively load balanced, but the FlowFiles never move. Listing or emptying the queue indicate that there are no FlowFiles. Upon restart, the FlowFile does not exist and the queue is cleared.