Is it actually a different server or just a different URL?
The different URL shouldn't mess it up. However, if it is a totally seperate server your session will be lost. However, there are several ways around this. One is to make the session files be stored on a shared drive that both servers can access. This is relatively simple and just requires changes to the PHP ini. This can lead to slower performance as reading from shared drives is not always the fastest operation.
Another (and probably better) option is to use session handlers that store the session data in the database. You can write them yourself or use some of the ones floating around on the internet. I actually believe there is an article (or 2) here on PHPbuilder about using database for sessions.
Good luck!