I have experienced syslog refusing to accept logs. But only on a syslog dedicated server. One where the syslogs of all the other servers are being sent. Since syslog is a udp service, it will drop data if it's coming too fast. Plus Solaris had a problem back in 2.5 or 2.5.1 where syslog would bail with door errors (it'd stay running but if you looked at the running process, you'd see door commands and then waiting). The solution was to apply a syslog patch that became available after some complaining
Oh and killing the daemon didn't fix it. You had to kill the daemon and delete the syslog.pid file or it'd stay lost.
Carl