CentOS 6 uses rsyslog 5.8.xxx which has rate limiting enabled. When too much comes in too fast, rsyslog says something like:
imuxsock begins to drop messages from pid $PID due to rate-limiting
Add to /etc/rsyslog.conf:
Note that this won't do anything to deal with losses that are udp-getting-dropped problems, but it raises the threshold of trouble somewhat higher than it otherwise would be.