Connection failure???

Hi, I have a general newbie kind of question. The server where my php/mysql site is being hosted keeps losing the MySQL connection, not just on my site but server wide. MySQL appears to be running when you enter ps ax | grep mysqld you get a reply: 9896 pts/0 S 0:00 sh /usr/bin/safe_mysqld --user=mysql --pid-file=/var/ 9913 pts/0 SN 0:00 /usr/sbin/mysqld --basedir=/ --datadir=/var/lib/mysql 10501 pts/0 SN 0:00 /usr/sbin/mysqld --basedir=/ --datadir=/var/lib/mysql 10513 pts/4 S 0:00 grep mysqld but when you try to access MySQL, you get a connection error. This is the 2nd time in the last 48 hours that this has happened. The ISP got it going for a moment and then it crashed again. My question is not how to fix it, but what might be causing this and how I can prevent it from happening when I recommend PHP/MySQL be installed on a client's server. I'm kind of worried that I chose the wrong tools. Any and all insights are appreciated. TIA, Beth