Outlook Works Badly With Wireless Network--Why?

It’s a puzzlement. We have three computers: two desktops running Windows 7 and a laptop running Windows XP. Two of these computers cannot, absolutely cannot, get Outlook to work with our mail provider (German GMX) while on the wireless network: a Windows 7 desktop and the XP netbook. Why should that be the case? The third computer, which had some trouble recently getting into my Microsoft Exchange mailbox, is running Outlook just fine while hooked up to the router by cable, but as soon as I activate its wireless, Outlook goes crummy: won’t connect to my Exchange server, won’t let me send (but WILL let me receive) my GMX mail.

Anybody got any idea? It’s not at all urgent (my GF keeps using online mail, and I’ve got my computer set up, as noted), but it’s a veritable puzzle to me, and incidentally, to my workplace’s IT support…

Thanks in advance for any suggestions (because I’m really bad about coming back in for the round of thanks later!).