I just found out today that my hosting company blocked my ip in there firewall due to too many connection requests.
One connection per second seems like an extremely low threshold...
isn't there some solid way of opening a connection and leaving it open so that the webserver isn't receiving connection requests every second?
Yes, but it requires the software running on the server and client to know about it. You might want to start looking at: http://en.wikipedia.org/wiki/HTTP_persistent_connection