This is ok. the connections are from several services like postfix, pureftpd, courier, amavisd etc. which all connect with the ispconfig user to the mysql database. ISPconfig itself uses just one connetion when you are logged into the interface and another connection when the backend starts the processing. both connections are closed right after the page has been delivered or the data has been processed. If you reach the max connection limit of mysql, this happens most likely when a lot of spam comes in. You can set a higher connection limit in the mysql my.cnf file.
Add or edit the following lines in the [mysqld] section of the file: