What are the hardware specs on your server, and what configuration settings have you made, and what add-ons (contribs) have been loaded?
Can you access the internet IP address from off-site after a failure (That is, is your WAN connection disconnecting for some reason)?
Can you still access the internet directly from the SME server (putty to your SME, 'ping google.com' or 'lynx google.com'). That is, has a SME service failed, or the internet connectivity from the sme itself?
Can you access off-site by IP address ('ping 64.233.167.99') Or, is it a DNS issue?
Is there anything interesting in any of the log files? (I'd look at /var/log/messages, /var/log/qpsmtpd/current, /var/log/squid/access.log)
Is your system out of disk space? (df -k)
[shame]I filled my disk last week and dns was the only service that failed -- but this prevented anything else from working...[/shame]