It's most likely that your office network connection has a firewall or is using NAT to connect to the internet. In this case your office server is not visible when you leave the office or it has a different address.
Thank you for your post.
If you are outside the local area network, then tap the new host icon and enter the IP Address of the host name. This should allow you to see the FileMaker files open on that server, unless there is a firewall in place (as mentioned by "pdh"). If a firewall is active, then you may need either a VPN connection or port forwarding.
What about 3g? Sounds imilar to my problem. I can connect with wifi but not 3g on my iPhone.