Too many connections [1040]

Hello,

since 2 weeks I have problems with the phpbb3 software. I thought it has something to do with my host but they told me it is the phpbb3 software. (also take a look at http://www.phpbb.com/community/viewtopic.php?f=46&t=547921 )
There are several other users that have this problem.

When there are to many connections it take also other parts of my website down.
These are the erros I could find:

---------------------------------
General Error
SQL ERROR [ mysql4 ]

Too many connections [1040]

An sql error occurred while fetching this page. Please contact an administrator if this problem persists.
---------------------------------

------------[ Begin General Error]------------
[04-Feb-2008 20:02:34 3600] [phpBB Error] [client ] [file ] /forum/includes/db/dbal.php:593
SQL ERROR [ mysql4 ]
Too many connections [1040]
An sql error occurred while fetching this page. Please contact an administrator if this problem persists.------------[ End of General Error]------------

Error in phpmyadmin
ERROR: Unable to connect to database: User admin has already more than 'max_user_connections' active connections 0: /usr/local/psa/admin/auto_prepend/auth.php3:67 psaerror(string "Unable to connect to database: User admin has already more than 'max_user_connections' active connections")

I have update from Phpbb2 at the end of december 2007.