A good DNS service is very important for a mail server.
On Linux servers you need to put your DNS servers on a file called resolv.conf. In general you have two entries like this:
nameserver1 192.168.10.10
nameserver2 10.10.1.1
If one server does not respond then linux will try the second, but there is a timeout for this:
timeout:n Sets the amount of time the resolver will wait for a response from a remote name server before retrying the query via a different name server. This may not be the total time taken by any resolver API call and there is no guarantee that a single resolver API call maps to a single timeout. Measured in seconds, the default is RES_TIMEOUT (currently 5, see <resolv.h>). The value for this option is silently capped to 30.
If you want to speed this resolution change resolv.conf to:
options rotate
options timeout:1
nameserver1 192.168.10.10
nameserver2 10.10.1.1
Using the configuration above, both nameserver in rotation and wait max. 1 second for answer before trying the next one.