In the POP3 settings, make sure that "Leave Messages on Server" is selected.
See Step 7 at this link: http://www.zawebhosting.co.za/page/evolution
Most POP3 clients have a setting of this type buried somewhere. In some, you can select how long to leave the messages on the server after you have downloaded them. When the deadline comes, the mail client deletes them.
Some mail server providers don't do IMAP for home use accounts. My ISP is one of them.