Using multiple machines to fetch mail from a POP account is dangerous. There's an option in most email readers to leave email on the mailserver for x days and then delete any messages it finds on the server that have been on your computer for at least that long, or are at least that many days old. There's also sometimes an option to remove messages you deleted on your machine immediately from the mailserver on next fetch.
Problem is, if you get mail from one for several days or a week straight, and then try to get mail on the other, it may have already deleted some new messages due to age before your 2nd machine gets a chance.
Some people configure their email apps to delete immediately after receiving in messages. That makes it a lot worse for the other computer because it misses a lot of mail.
If you don't want this behavior, you really need to use IMAP. IMAP keeps a copy of all messages on the server unless you tell it otherwise or move them to a local mail folder. IMAP has the danger though of overflowing your mailserver capacity limit if you frequently receive email attachments, or if you just don't delete email often. (or forget to empty the IMAP's trashcan! we see that a lot)
