How do you connect?
With HTTP-tunnel every query creates a new connection. That is not a SQLyog issue, but a PHP issue!
However you can try changing the _connect to _pconnect in the tunneller as described here:
http://webyog.com/faq/21_103_en.html
If you need help, please write back.
Can't you simply raise that setting? Normally it is set as “0” – meaning “no limit”.