Having exact the same issue. This basicly happened after updating to 4.6.7.
Now I have a load of clients (thousands), and it is creating a load on the SQL CPU as well. When shutting down the Apache service on the Application Server it drops immediatly.
Am already struggling with this for over a month and ticket is outstanding for that time as well with McAfee (they are currently preparing a fix according to the ticketting system).
I think there was a serious glitch in the 4.6.6 upgrade towards 4.6.7 where they are now aware of.
Logs on update was clean and perfect, yet very strange behaviour not long after.
Having also issues on sitelists messing up at times.
My best guess for you as well, have a ticket done, as this is not normal behaviour. I upgraded my labserver a few weeks before with none of these issues at all. => beats me.
Even have a secondary labserver running in 5.1 (green setup) with absolutely no issues like this going on.
Good luck on getting there, I will let you know if the fix will work (dont have it yet), so you can refer to it when it does.