Using Brickhouse's log function I found the port which is used to set up the connection. I then added an Allow filter which allows TCP traffic from 10.0.1.2 through 10.0.1.9 to my computer on port 548. Bingo! Connect to Server works again!
Note that I can be specific about the ports because the maximum number of machines served by the Airport is 4. However, they use DHCP to get their IP addresses so allowing between 2 and 9 is fine.

