Did you find this comment on d.o: http://drupal.org/node/474152#comment-1779744 ?

It explains how to set a per-user limit and increase the number of files that can be opened. If you don't have enough memory in the server there may not be many options, however.

Did you find this comment on drupal.org?

The problem is a maximum open files limit per users.
We had several web servers, and several new Apache2 VirtualHost; Apache2 (www-data) reached the maximum number of open files (1024).

You can check that with ulimit -a or ulimit -n. (The default is maximum 1024 open files.)

You can modify it with ulimit -n 1500, but it will be lost after reboot.

To make the change permanent, add in /etc/security/limits.conf:

#<domain> <type> <item> <value>
#
www-data soft nofile 1600
www-data hard nofile 65535

Of course, restart your web server.

It explains how to set a per-user limit and increase the number of files that can be opened. If you don't have enough memory in the server, there may not be many options.