DB Connectivity Problem

Does anyone have any suggestions for the following problem:

I'm running Apache/1.3.31 and PHP Version 4.3.8 connecting to an Oracle
database. Periodically, PHP is unable to connect to the database. When this
problem occurs, I am able to connect to the database from the webserver
without any problem using SQLPlus. I've also run tcpdump on my database
server and I see no incoming requests from the problem web server when I run
a PHP page that queries the database.

A graceful restart of apache, or simple 'apachectl restart' do not fix the
problem. I have to manually stop and start the apache process and the
problem goes away (for a while at least).

We are using persistent database connections, but non-persistent ociconnect
calls also fail. The number of DB connections is unlimited in the php.ini
config. Also, my DB server has plenty of capacity to accommodate many more
connections.

Thanks,

Jon