Adding DHCP reservations breaks port forwarding with Airport Extreme

I have discovered after a lot of trouble that port forwarding breaks on my brand new Airport Extreme when I assign a DHCP reservation using a MAC address. If I forward a port with the automatic DHCP reservation, port forwarding works fine. Once I assigned a reservation, port forwarding ceases to work. SSH outputs: Network is unreachable.

I have tested this with a Macbook Air and Linux desktop with the same results.

I realize this can be resolved with static IPs, but I didn't shell out $250 for a new router for it not to work. Also it took me a week to figure this out.