Error with DataBase

Hi! I have moved my wordpress blog to a diferent host, and now SOMETIMES for a few seconds, or a minute, when i want to acces the site or something in it, i get:
“Error establishing a database connection”

And there is no error with the username, password or localhost in wp-config.php, because it runs like he should most of the time. But, sometimes like i said i get this error, and i want to fix it if there is a way to do this.

Any idea? ??