Thanks very much for this answer. It will help me have a more constructive dialog with my hosting service. They offered to migrate my sites (I have a second similar site for a different alumni body, which is having the same problems) to a different server with less traffic. I will refer them to the article you referenced. I will ask them to run the commands:
echo 8192 > /proc/sys/fs/file-maxecho && 32768 > /proc/sys/fs/inode-ma +x
ulimit -a
ulimit -n
ulimit -H
I would also like to try inserting
warn `ls -l /proc/$$/fd/` . ' ';
into the 3 most popular modules in the script. Finally, thanks for the suggestions on not capitalizing Perl. I had no idea. The last thing I want to do is offend the very people from whom I need help.

In reply to Re^4: How to debug "Too Many Open Files" Error by tonyb48
in thread How to debug "Too Many Open Files" Error by tonyb48

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