said by Rattler :

Or, you can just set up your email clients independently on both machines and keep two (or more) local copies of your email databases. Set one machine's client (the main one) to leave the mail on the Verizon POP server for a week or two and set the other to leave the mail on permanently. That way, only one controls mail removal from the server and the other leaves it alone. Leaving the mail on the POP server for a week or so, allows for a window for the "slave" client(s) to get the mail before it is removed. This is what I have been doing for quite a while.

My main machine leaves the mail on for 7 days, the second one doesn't do anything about removing it from the POP server and my laptop is set up the same way. I only care about mail on the laptop when I'm on the road. If I need to synchronize the email database on the laptop, I simply copy over the data files from the main machine. I use Eudora so it's not difficult to figure out which files are needed.

This "compartmentalized" method also works well if you use two or more different email clients. e.g. Eudora or T'bird or Outlook/Express where they can't conveniently share the email files.