CGI-Limits

I have been through the forum a number of times in regards to:

CGI-limits reached, please try again later!

We have moved to a dedicated server, got rid of all unwanted plugins, increased the memory on the sites that use the most plugins and still all the sites go down together as they are hosted in the same space around 11am and 6pm everyday.

The hosts are logging the server, but the server isn’t physically going down. I am running memory plugins but I need help finding the needle in the haystack.

I have seen some people mention php.ini? Any help would be great.