If you're in the middle of a transaction and haven't posted it, and for any reason you lose your connection to FA such that you have to start over, then yes the current data for that transaction will be lost. One thing you can try, though, is to use the "back" button in your browser to get back to the page you were one and try refreshing it. That may re-insert your data into the fields from your browser's cache. It may not, too, though, so there's no guarantees.
Having said that, I'm unclear why FA running on a server using a dynamic IP would drop the connection? The ISP's DNS server should always properly resolve the URL to the proper IP address, even if it changes. Sounds to me like there's an issue with your ISP's DNS server. What specific error message are you getting when the connection drops? Are you sure it's a DNS problem and not a web server (apache or whatever) problem?
Hope that helps...
Regards,
Chris