Reached MaxCients setting, but no traffic!

I'm renting a somewhat powerful server with 12GB of RAM and twin xeon cpus running ubuntu 10.04 x64. I installed apache and mysql, I loaded the mod_rewrite module, and the site works fine!

Until a couple of hours when the site becomes unresponsive. I'm still able to SSH into the server, I look at the error log and I see this:

server reached MaxClients setting, consider raising the MaxClients setting

But apache serves maybe 10 visitors a day! The memory has barely been touched, as well as the cpu. I raised the maxclients setting to 800 where possible. Here are my current settings:
<IfModule mpm_prefork_module>
ServerLimit 800
StartServers 5
MinSpareServers 5
MaxSpareServers 20
MaxClients 800
MaxRequestsPerChild 0
</IfModule>
<IfModule mpm_worker_module>
ServerLimit 800
StartServers 2
MaxClients 800
MinSpareThreads 20
MaxSpareThreads 75
ThreadsPerChild 20
MaxRequestsPerChild 0
</IfModule>
<IfModule mpm_event_module>
ServerLimit 800
StartServers 2
MaxClients 800
MinSpareThreads 25
MaxSpareThreads 75
ThreadLimit 64
ThreadsPerChild 25
MaxRequestsPerChild 0
</IfModule>
If I restart Apache, the site works for another couple hours until I get the same MaxClients error. Any help would be very much appreciated, I can't let this server suck up my money while being useless.

Why did you set MaxRequestsPerChild to 0? If you do that the child process will never terminate. Which is probably how you are maxing out the number of connections.

See: http://httpd.apache.org/docs/2.0/mod/mpm_common.html#maxrequestsperchild

Why did you set MaxRequestsPerChild to 0? If you do that the child process will never terminate. Which is probably how you are maxing out the number of connections.

See: http://httpd.apache.org/docs/2.0/mod/mpm_common.html#maxrequestsperchild

I changed it to 900, and the same error occurred again.