Seems like one of the problems with my current home server setup is that it's using itself as the DNS server. (Without backup DNS) Don't know if this is the root of all its problems, but at least it explains why I don't get log mails anymore. Now trying to fix this by changing the network interface configuration made it disappear from the network all together. <Sigh> Down to the basement then.
@Chaos_99 Local DNS server with properly configured forwarding might be really reliable configuration if done properly. For example cached records can be returned even if the network interface is down. I usually do this with firewalls and other systems that tend to do a lot of DNS queries.