Sounds like your problem is in the PHP or Java (or whatever language) you're using to dynamically create those pages.
The basics are you obviously have an amount of memory per connection and number of connections. If the number of connections is raising continuously then your problem is in why it's not releasing those connections.
Apache by default (and various other web server technologies) will drop a connection after enough time last elapsed if it's inactive, so unless you have more and more people constantly building up on your site then either you disabled this default behavior (unlikely as you would've have to have done it on purpose), or (more likely) there's some infinite loop typoe logic in some code on your pages that is eating up memory and keeping apache thinking the connection is alive.
Review what you've custom coded and google around on any third-party add-ons to see if they have known memory issues. One or the other should solve it.