Screen Saver/Login Manaager
I have Fedora 6 and have not seen the Fedora 2 interface, and do not know exactly how the main system menu appears. On Fedora 6, it's an icon with a stylized "f". Off of that menu, there should be a system menu, with a subdivision after that for Preferences and Administration.
Start with preferences and screen saver, or if there is a pick for login management, try that. It sounds like your screen saver is logging you out after a time.
If not, think about upgrading -- new install -- to whatever the latest Fedora is, unless your hardware requires an older version of the OS. I'm moving my last test machine (Fedora 6) to CentOS, because that will map to our RHEL systems, and it requires no "entitlements". Fedora's updates stopped too quickly for me.
If this is older hardware and you are not tied to development or applications that depend on Fedora, think about Xubuntu or Zenwalk.