What do you see in the logs when it (dns: udp 53) fails?
Is this traffic allowed by the acl applied on the ingress interface?
pls. enable logging:
conf t
logging enable
logging buffered 7
exit
sh logg | i x.x.x.x
where x.x.x.x is the host on the inside that has trouble with dns.
Besides the above you can apply captures on the ingress and egress interface to see if we are sending the resquest out the outside interface and if the response is seen or not.
You can refer this link for packet captures:
http://analysisandreview.com/cisco/how-to-configure-a-packet-capture-in-the-cisco-asa/
