Shouldn't be happening if you're using POP from OE.
It doesn't happen for me, using squirrelmail on the server to read email, and KMAIL (linux/kde/konqueror) to download the mail without deleting it from the server.
However...
Look to make sure you haven't got something checked for "delete from server when deleted locally" or something like that. Some mail clients have that; I believe Eudora can do that, but I don't know about others. If it's enabled, then if you delete the emails in OE they'll be deleted from the server.
Also if you're using IMAP with OE deleting the emails locally will delete them on the server.
Jeff