Hi I'm having a really strange issue which is quite critical as this system is used 24/7.

What happens is eth0 becomes unresponsive. Can't SSH, can't access using HTTPS. Nothing in the logs indicates in issue, the machine says the interface is up. Sometimes after 30 minutes, it will magically start working again. I have found that doing service networking restart will cause the interface to work about 30-60 seconds after the restart has completed.

I'm happy to provide any info but I really don't know where to start. I'm not sure if it's a DNS issue, hardware issue, driver issue, software bug. Could it even be a faulty cable?

So isolate things one by one.

You can use a Livecd to check whether it's installed software issue.

I lose connections sometimes, and I don't know why (It probably has to do with my cable-modem) but here is the command I enter:

sudo /etc/init.d/dnsmasq restart && sudo ifdown eth0 && sudo ifup eth0

It works for me. However, you mileage may vary.