MySQL can “freeze” or become unresponsive and a query coming from WordPress could be responsible for it. That’s why I suggested monitoring the database, this includes logging such queries that take a long time to execute.
As your host has Fantastico, there should also be a control panel (cPanel for example). From within this control panel, you can set a new password for the DB user.
The server admins should be able to narrow down what causes the database to crash, by monitoring MySQL along with some system parameters. I’d say it’s unlikely that you’ll be able to fix the problem within WordPress.
Most likely the database engine (MySQL) needs some tweaking and you (or your server admin) need to find out why it crashes. For example, the server might run out of memory while many people visit your blog at the same time. So chances are that’s rather a server tuning issue than a WordPress problem.