linux - Server crashing: Too many connections?

I have server with approximately 500 active connections at a time (it's for a very busy website). Unfortunately, Apache keeps crashing the entire server every hour or so. The server has 8 GB of RAM and a quad core Xeon CPU so, as far as I am concerned, this should be sufficient to handle the amount of connections. I suspect that my Apache configuration could need some optimization. Here is the current config:

StartServers          2
MinSpareThreads      25
MaxSpareThreads      75 
ThreadLimit          64
ThreadsPerChild      25
MaxClients           400
MaxRequestsPerChild  20000

Any advice (not only related to Apache) is MUCH appreciated!