Mysqldump error 1017: errno: 24 - help?

[Mysql user]

Hi.. 

I've got an ISP, and all of our customers have databases in our mysql
system. 

My backup command is:

mysqldump --force --opt -A -pxxxxxxxx' | gzip -c >
/var/sqlbackup/mysqldump-`date +\%A`.sql.gz 

This has worked fine for some time. 

Now, however, I get an error message: 

mysqldump: Got error: 1017: Can't find file:
'./usr_web22_1/invoices_va.frm' (errno: 24) when using LOCK TABLES 

On different runs, it reports different files, even right after
restarting mysqld.

I've looked at the mysql documentation for this error; it's at 
http://dev.mysql.com/doc/mysql/en/Not_enough_file_handles.html

I've looked at the startup script, put in '--open-files-limit=1024',
restarted mysql, and the error is the same. 

I've looked at the table_cache and max_connections system variables,
which are 64 and 100, respectively. 

My question is: what should I do now? 

Since table_cache and max_connections are far less than 1024, do I
reduce them even further? 
Is there something else I should be looking at? 

This is mysql-3.23.52-106 on SuSE Linux 8.1, running on a dual PIII
866Mhz system, with 512M of ram and 1G of swap, on a RAID-1 pair of 17G
hard drives.

Thanks!