[freakshow]

it sounds like you know what you're doing..
As you said, you need to set the computer's IP to a static IP outside of the DHCP range.
You should do this at the router level as well (leave the computer as dhcp). Tell the router to assign a certain IP to the computer based on the computer's MAC address. Each time the computer connects to the router, it'll get the same local IP back.

edit: just re-read your post.. you mean that the computer (with the program) and the router will both be changing quite often? If that's the case.. I'm not sure what you can do.. if you change the computer and router.. of course *something* is gonna have to get reconfigured..