How To Find Reasons of Why Site Goes Online/Offline

Solution 1:

The load average in the 30s is high and the CPU is 100% busy. CPU usage is pretty even across your HTTPD processes so it's not one specific rogue process. Basically your server is not capable of handling the number of concurrent HTTP requests it is receiving.

It may be that you could do something to reduce the amount of processing needed to produce a page.

You could review the Apache server logs to try to see why the loading is so uneven. Perhaps you are being targetted by a DDOS attack - if so there are things you can do to mitigate the effects.

Either that or you need a bigger server.

Maybe MediaTemple have a problem - see How do I optimize a high traffic Wordpress website?