Error message: 
Destination queue full, dropping messages; queue_len='10000', 
log_fifo_size='10000', count='4', 
persist_name='afsocket_dd_qfile(stream,serverdown:514)'
Description:

This message indicates message loss.

Flow-control must be enabled in the log path. When flow-control is enabled, syslog-ng will stop reading messages from the sources of the log statement if the destinations are not able to process the messages at the required speed.

If flow-control is enabled, syslog-ng will only drop messages if the destination queues/window sizes are improperly sized.

Solution:

Enable flow-control in the log path.

If flow-control is disabled, syslog-ng will drop messages if the destination queues are full. Note that syslog-ng will drop messages even if the server is alive. If the remote server accepts logs at a slower rate than the sender syslog-ng receives them, the sender syslog-ng will fill up the destination queue, then drop the newer messages. Sometimes this error occurs only at a specific time interval, for example, only between7:00AM and8:00AM or between16:00PM and17:00PM when your users log in or log off and that generates a lot of messages within a short interval.

For more information, see Managing incoming and outgoing messages with flow-control.