Try adding this piece of code to the page you are getting the error:
<?php
$link = mysql_connect("localhost", "mysql_user", "mysql_password");
if (mysql_errno() == 1203) {
// 1203 == ER_TOO_MANY_USER_CONNECTIONS (mysqld_error.h)
header("Location: http://your.site.com/alternate_page.php");
exit;
}
?>
i got that code from this page:
too-many-connections.html
It is definitely something that you would have to resolve with your hosting provider. Unless there is a loop that is trying to connect to the database every time which i don't think it is the case here.