Too many open files

I'm hoping that I will be coming to the end of the issues. After a new client with a heavily spammed email domain got pointed to the server I have had tons of issues. The latest is:

Feb 24 15:57:11 virt3 postfix/master[2740]: warning: /usr/lib/postfix/tlsmgr: bad command startup -- throttling
Feb 24 15:58:01 virt3 /USR/SBIN/CRON[19910]: (root) CMD (/usr/local/ispconfig/server/server.sh > /dev/null 2>> /var/log/ispconfig/cron.log)
Feb 24 15:58:08 virt3 mysqld[2132]: 100224 15:58:08 [ERROR] Error in accept: Too many open files in system
Feb 24 15:58:11 virt3 postfix/master[2740]: warning: master_wakeup_timer_event: service pickup(public/pickup): Too many open files in system
Feb 24 15:58:11 virt3 postfix/anvil[20329]: fatal: epoll_create: Too many open files in system
Feb 24 15:58:12 virt3 postfix/tlsmgr[20330]: fatal: tls_prng_exch_open: cannot open PRNG exchange file /var/lib/postfix/prng_exch: Too many open files in system
Feb 24 15:58:12 virt3 postfix/master[2740]: warning: process /usr/lib/postfix/anvil pid 20329 exit status 1
Feb 24 15:58:12 virt3 postfix/master[2740]: warning: /usr/lib/postfix/anvil: bad command startup -- throttling
Feb 24 15:58:12 virt3 postfix/master[2740]: warning: process /usr/lib/postfix/tlsmgr pid 20330 exit status 1
Feb 24 15:58:12 virt3 postfix/master[2740]: warning: /usr/lib/postfix/tlsmgr: bad command startup -- throttling

 

I have done an lsof, and there are 1000's of lines.