php数据库连接错误

im hoping someone can help me quickly with a question i have.

As site i have build is occasionally returning with the error

Warning: mysqli::mysqli() [mysqli.mysqli]: (08004/1040): Too many connections in

Warning: mysqli::query() [mysqli.query]: Couldn't fetch mysqli in

Now at first i thought this was happening as i hadent closed the connection at the end of each page, now i get the connection like this at the beginning of a page / script

$conn = new mysqli($host, $username, $password, $database);

and at the very end call

$conn->close();

Also i close any result sets i have open.

Looking at my log files around the time i accessed the site today and saw this error, I accessed about 12 o clock and at first the page wouldnt even load, then it gave me this error. before that one person visted around 11:30 and then 10:30, not exactly heavy traffic.

The host I have gone with is very quiet and there is no way to get in contact with them, and ignoring any support emails, i thought maybe as now i hear they are not very good this could be an issue with a badly set up shared mysql server?

Any thoughts or suggestions would be amazing as i need to sort this out!

Thanks in advance!