Frequent mDNSResponder host resolution issue

I have a frequent problem with one specific host on my network. I have a local DNS server running on one of the machines. I have host nas.mydomain.com configured through that DNS with A and AAAA records. So far so good. I am using this nas storage as a time machine disk for backups from my macbook pro running OSX Mountain Lion. So far so good. The problem is that rather often I receive message "Backup disk is not available".

When this happens, I can no longer access the server via web browser, ping it, ssh to it or traceroute to it - I get the same message "host not found" (or such like).

The DNS server is running find and the host is resolvable, as in the terminal, dig, nslookup and host find the host with no problem. mDNS negative caching is set to 1 hour and TTL is set to 24 hours.

Once this error appears, it does not go away on its own (I tried witing for 24 hours). If I kill -SIGHUP the process of mDNSResponder, then everything works correctly again - for a few hours, after which the problem comes back.

Is there a permanent solution to this issue?

Note that I cannot upgrade to a newer version of OSX due to incompatibilities with a number of legacy software used on this mac, which doesn't support anything beyond Mountain Lion.