Intermittent fault with connection to website

I have a weird issue.
Our server setup is a 7 server cluster, with various sites across it.
There are a couple of different IP's which certain sites use one, some the others etc.

Now, the site in question I sometimes can't connect to is my main domain on the cpanel account, which has 2 other add-on domains.
Sometimes when I cannot connect to the main site, I can connect to one of the addon domains. Which to me is weird as the addon domain is a sub-folder in the main site's folder.

When I cannot access with http:80, I also cannot ping that domain or get emails from it (OS client).

While connection is lost, I also cannot connect to SOME other sites on our server (outside my cpanel account) and some I can. The IP of the websites I can and cannot connect to carries no pattern.
I.E. It's not just problematic with all sites on one IP and not the others.

The fact I have never found any issues at all with other sites not on our server even while connection is not available to my sites leads me to our server setup/DNS or configuration setup somewhere.
But to blow that idea out of the water, if I use a public proxy I can connect to all my sites straight away, always and without any issues even when connection is lost with direct connection.

I first suspected a DNS issue, but intermittent? That's unlikely IMO with DNS.
Sometimes 30 mins can pass where I cannot connect and sometimes only a few minutes, 5 or 10 mins.
Sometimes after regaining the ability to connect, it can be lost again anywhere from 3 to 4 mins up to hours or days.
There are no time patterns for all the different time durations for connection loss and time passed before connection is available again.

Sometimes connection ability comes and goes 5 or 6 times in a few hours, and 20 or 30 times a day, and sometimes days pass by without any issue at all.

I still think it cannot be DNS with it being so intermittent and also the fact it sometimes comes back online after only a few mins. But the fact I can always connect if I use a proxy (which of course will use different DNS servers to my ISP connecting direct) makes me think towards my ISP DNS.

My ISP uses a range of different DNS servers (I believe is how it works) and this changes each time I connect to a website (I believe this also happens, a DNS server from a range of choices is chosen at random) so perhaps some of their DNS servers on route are buggered.
Bad DNS lists or whatever.

It did the same sometimes when I used win XP, am now on Ubuntu. So it's not likely a software/browser/OS or network issue or even settings.

This is driving me nuts. Any ideas?