The only way around this is to set one (the laptop) or both computers to Leave a Copy on the Server. If that is not set the first computer downloads the mail and the second will have nothing to download. Just be sure to set the length of time to keep the mail on the server if you have both computers set to leave mail on server so the server does not get clogged with old mail. I would set the desktop to collect the mail and NOT leave it on the server, while the laptop always leaves it on the server. 
Help please!  I currently have a laptop and desktop PC and am using Outlook 2010 on the laptop and Windows Mail on the PC to check email from my talktalk account.  While the PC is able to receive all the emails, the laptop seems only to display emails sporadically - is this because the PC was the original machine that I set up to receive emails, or is there something I can do to enable both machines to receive all emails?  Any help gratefully received!!!
Problems receiving emails