Perhaps you could use something based on HTTP::Daemon. merlyn has a few excellent articles on his web site doing something similar using Chatbot::Eliza. Check out the articles with a title like "Doctor is IN", namely Column 23 and Column 24.

The idea is that you have one script that starts out as a CGI, which contains the actual state, and which launches its own small webserver — and keeps running in the background. That one takes over for this session, processing all following requests from the browser, and all in the context of the current application.