Is there a high cpu load when the website goes down? What processes are causing it? Is there a high RAM usage at that time? You can watch the load "live":
Code:
# MYSQL_PWD=`cat /etc/psa/.psa.shadow` watch "uptime && echo "\ " && ps aux | sort -nrk 3,3 | head -n 20 && echo "\ " && mysqladmin proc status -u admin"