The whole thing sounds a little strange. One of the points of using a DHCP server is that the server doles out IP addresses such that there are no conflicts. I'm not totally sure about the Airport base station, but I believe that most DHCP servers are designed to try to give every computer the same IP every time. It should only drop the association when it runs out of IP addresses. Either way, as long as the servers are running, their IPs should never change.

Further experimentation found that, regardless of what IP I put in, it would not retrieve anything from the AEBS. Apparently DHCP w/manual IP just does not work with the AEBS.