420 Too Many Open Files

I'm running Apache 2.2 under OS X Server 10.5.2. In the wake of Security Update 2008-002, Apache refuses to run, with the following log entries:

[Wed Mar 19 17:01:16 2008] [notice] Graceful restart requested, doing restart
[Wed Mar 19 17:01:16 2008] [error] (9)Bad file descriptor: apr pollsetpoll: (listen)
piped logspawn: unable to setup child process '/usr/sbin/rotatelogs "/Services/Laughing Boot/Sites/Logs/defaultsite/accesslog" 604800 -420': Too many open files
Unable to open logs
[Wed Mar 19 17:01:20 2008] [warn] pid file /var/run/httpd.pid overwritten -- Unclean shutdown of previous Apache run?
[Wed Mar 19 17:01:20 2008] [error] (24)Too many open files: could not create /var/run/httpd.pid
[Wed Mar 19 17:01:20 2008] [error] httpd: could not log pid to file /var/run/httpd.pid

The last three lines repeat, ad infinitum.

I have forty-some sites, and if I disable all but 33 of them, the problem vanishes. Enable 34, and the above fit ensues.

As you can no doubt tell, this all a bit over my head. I'm pounding my head against the espresso machine and shortly will begin moaning about how God hates me.

Anyone care to at least point me in the right direction?

Thanks,
Bryan