Hard to say without knowing more about your server and traffic load, but doesn't sound right to me. Never heard of particular issues with EE/apache. Extremely rare for apache to max out cpu before mysql does, with varnish on the frontend acting as cache it should be serving most requests without any connection to apache - I'd check it's configured correctly and that you're getting a good cache hit rate.
I agree with EastCoast, the DB will run out of available connections/ max cpu usage before PHP/ Apache do. Perhaps you're simply having a lot of traffic on a server that is no longer up to the task of handling all the traffic (even with Varnish in place)?
Maybe it's time to throw some extra hardware at it
Just be aware, that throwing more hardware at the problem MAY not be the entire solution... in the case of a forum I'm involved with, Jelsoft's answer was to throw more hardware at it, that was 2 years ago - we're still running on the same, single server when they claimed we'd need 4 to run the setup.
Is it possible there are some queries in the code that could be optimised to improve the sites performance?
Unfortunately I have the same problem in a number of the hosting companies. CPU of expression engine and RAM usage is extreme. What I am looking now is to find somebody who can help me change the platform and move in Word Press.