Here is what my log indicates at the time of the problem (I will work on the zend upgrade but I don't think that is it because I was having the same issue before I upgraded my PHP a few months ago.
[Sat Apr 10 07:37:35 2010] [notice] caught SIGTERM, shutting down
[Sat Apr 10 07:37:36 2010] [notice] suEXEC mechanism enabled (wrapper: /usr/sbin/suexec)
[Sat Apr 10 07:37:36 2010] [warn] RSA server certificate CommonName (CN) `plesk' does NOT match server name!?
[Sat Apr 10 07:37:36 2010] [warn] RSA server certificate CommonName (CN) `plesk' does NOT match server name!?
[Sat Apr 10 07:37:36 2010] [notice] Digest: generating secret for digest authentication ...
[Sat Apr 10 07:37:36 2010] [notice] Digest: done
[Sat Apr 10 07:37:36 2010] [notice] LDAP: Built with OpenLDAP LDAP SDK
[Sat Apr 10 07:37:36 2010] [notice] LDAP: SSL support unavailable
PHP Warning: Zend Optimizer does not support this version of PHP - please upgrade to the latest version of Zend Optimizer in Unknown on line 0
[Sat Apr 10 07:37:37 2010] [notice] mod_python: Creating 4 session mutexes based on 10 max processes and 0 max threads.
[Sat Apr 10 07:37:37 2010] [warn] RSA server certificate CommonName (CN) `plesk' does NOT match server name!?
[Sat Apr 10 07:37:37 2010] [warn] RSA server certificate CommonName (CN) `plesk' does NOT match server name!?
[Sat Apr 10 07:37:37 2010] [notice] Apache/2.0.52 (CentOS) configured -- resuming normal operations
[Sat Apr 10 07:37:46 2010] [error] server reached MaxClients setting, consider raising the MaxClients setting