There are two kinds of cookies; file-based and memory.  PeopleSoft stores information in memory cookies that could assist with knowing which web server your user has connected to.

While on a PeopleSoft page, type the following in the url to see your memory cookies:

javascript:alert(document.cookie);

This is handy when your system has more than one web server, and you believe that the issue happens on one or a portion of your web servers.