>After random periods of time I am no longer able to pull up web pages 
>based on their FQDN (Like I can't access http://m0n0.ch/wall) or 
>(www.apple.com) but I could use their IP addresses to reach these 
>sites.  What is odd is that I can still ping these sites and recover 

You wouldn't happen to be using Comcast?  I know Comcast has been having
issues with their DNS server lately.  If you have m0n0wall setup to use DHCP
on the WAN side, it will use Comcast's DNS server.  Use a root server IP
address instead or some other ISP DNS server.  Regardless it does sound like
a typical DNS server problem.