You could also be hiting the Apache timeout configuration value, since I think ulimit is for all the process and cannot be aplied to just a process (or class of process, like Apache childs).

By default, Apache comes with a 300 seconds timeout for browser/server comunication, as can be seen from a httpd.conf :

#
# Timeout: The number of seconds before receives and sends time out.
#
Timeout 300

If this is the case, then there's an article writen by Randal Schwartz (merlyn here at PM) for Web Techniques (hi Randal, love your articles ;-) that talks about how to have a browser keep asking for incremental results whitout actualy being always connected and hiting the timeout.