I administer a RHEL server, which until recently was running RHEL 5.something. I had public keys set up so I could connect to this server from my desktop without a password (using keychain to manage ...

I don't use passphrases nor ssh-agent; most of my coworkers who do end up having issues. It's finicky. So all your tests are run within the same terminal, right? I would try to find out which ssh ...