my connections never die

I'm running a web server on one machine (Apache 1.3+Tomcat 3.2+mod_jk)
with some databases (postgresql 7.1), and a dedicated database server on
another machine (postgresql 7.0.2). A lot of my web pages establish a
connection to a database on either machine and store the Connection
object in a session so's I don't have to create a new one every page.
Well, it seems these connections, which never get explicitly closed, are
never dying. Some of them, anyway. I haven't been able to predict
which ones are going to close themselves and which ones will stay open
for days, but some of them are still taking up a process days later.

Greatly appreciating any explanation,
Ben Carterette
bcarterette(at)mail(dot)liberty(dot)k12(dot)mo(dot)us