It sounds like you're not in a persistent environment. If that's right, give this a look--FCGI--and check to see if your host is running one of its engines/drivers on your webserver. It would help; maybe a lot.

If it's really a problem with too many connections, you should investigate streaming/sending the content to them differently. This is a big problem space in which I'm not adept and the best/easiest solution is likely not going to be Perl-oriented; you might get a good direction/approach from another monk here.