Database error after a few hours running

Hi everybody,
I’ve moved my wordpress blog from a shared hosting to a VPS. Everything runs quite fine when the system is started, but after a few hours there is a performance decay and then the blog crashes with an “Error establishing connection to database” error.
I’ve already installed WP-SuperCache, and it helped a bit to have the server lasting a bit longer, bud did not solve the problem.

I think this could be a MySQL misconfiguration problem (I have default server setting, by now): anybody knows where is possible to find a guide to WordPress-oriented MySQL configuration… or even better had similar problems and knows if the settings that could solve this kind of problem?

Thank you in advance!